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A 23-ft ladder leans against a building so that the angle between the ground and the ladder is 80° . How high does the ladder reach up the side of the building?

22.6506 ft

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The angle of elevation to the top of a building in New York is found to be 9 degrees from the ground at a distance of 1 mile from the base of the building. Using this information, find the height of the building.

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The angle of elevation to the top of a building in Seattle is found to be 2 degrees from the ground at a distance of 2 miles from the base of the building. Using this information, find the height of the building.

368.7633 ft

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Assuming that a 370-foot tall giant redwood grows vertically, if I walk a certain distance from the tree and measure the angle of elevation to the top of the tree to be 60° , how far from the base of the tree am I?

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Review exercises

Angles

For the following exercises, convert the angle measures to degrees.

For the following exercises, convert the angle measures to radians.

Find the length of an arc in a circle of radius 7 meters subtended by the central angle of 85°.

10.385 meters

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Find the area of the sector of a circle with diameter 32 feet and an angle of 3 π 5 radians.

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For the following exercises, find the angle between 0° and 360° that is coterminal with the given angle.

For the following exercises, find the angle between 0 and 2 π in radians that is coterminal with the given angle.

20 π 11

2 π 11

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For the following exercises, draw the angle provided in standard position on the Cartesian plane.

Find the linear speed of a point on the equator of the earth if the earth has a radius of 3,960 miles and the earth rotates on its axis every 24 hours. Express answer in miles per hour.

1036.73 miles per hour

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A car wheel with a diameter of 18 inches spins at the rate of 10 revolutions per second. What is the car's speed in miles per hour?

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Unit Circle: Sine and Cosine Functions

Find the exact value of sin π 3 .

3 2

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Find the exact value of cos π 4 .

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Find the exact value of cos π .

–1

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State the reference angle for 300° .

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State the reference angle for 3 π 4 .

π 4

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Compute cosine of 330° .

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Compute sine of 5 π 4 .

2 2

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State the domain of the sine and cosine functions.

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State the range of the sine and cosine functions.

[ 1 , 1 ]

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The Other Trigonometric Functions

For the following exercises, find the exact value of the given expression.

For the following exercises, use reference angles to evaluate the given expression.

If sec ( t ) = 2.5 , what is the sec ( t ) ?

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If tan ( t ) = 0.6 , what is the tan ( t ) ?

0.6

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If tan ( t ) = 1 3 , find tan ( t π ) .

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If cos ( t ) = 2 2 , find sin ( t + 2 π ) .

2 2 or 2 2

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Which trigonometric functions are even?

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Which trigonometric functions are odd?

sine, cosecant, tangent, cotangent

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Right Triangle Trigonometry

For the following exercises, use side lengths to evaluate.

cos ( π 2 ) = sin ( __° )

0

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csc ( 18 ° ) = sec ( __° )

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For the following exercises, use the given information to find the lengths of the other two sides of the right triangle.

cos B = 3 5 , a = 6

b = 8 , c = 10

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For the following exercises, use [link] to evaluate each trigonometric function.

A right triangle with side lengths of 11 and 6. Corners A and B are also labeled.

For the following exercises, solve for the unknown sides of the given triangle.

A 15-ft ladder leans against a building so that the angle between the ground and the ladder is 70° . How high does the ladder reach up the side of the building?

14.0954 ft

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The angle of elevation to the top of a building in Baltimore is found to be 4 degrees from the ground at a distance of 1 mile from the base of the building. Using this information, find the height of the building.

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Practice test

Convert 5 π 6 radians to degrees.

150°

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Convert −620° to radians.

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Find the length of a circular arc with a radius 12 centimeters subtended by the central angle of 30° .

6.283 centimeters

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Find the area of the sector with radius of 8 feet and an angle of 5 π 4 radians.

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Find the angle between and 360° that is coterminal with 375° .

15°

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Find the angle between 0 and 2 π in radians that is coterminal with 4 π 7 .

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Draw the angle 315° in standard position on the Cartesian plane.

A graph of a circle with an angle inscribed.
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Draw the angle π 6 in standard position on the Cartesian plane.

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A carnival has a Ferris wheel with a diameter of 80 feet. The time for the Ferris wheel to make one revolution is 75 seconds. What is the linear speed in feet per second of a point on the Ferris wheel? What is the angular speed in radians per second?

3.351 feet per second, 2 π 75 radians per second

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Find the exact value of sin π 6 .

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Compute sine of 240° .

3 2

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State the domain of the sine and cosine functions.

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State the range of the sine and cosine functions.

[ 1 , 1 ]

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Find the exact value of cot π 4 .

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Find the exact value of tan π 3 .

3

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Use reference angles to evaluate csc 7 π 4 .

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Use reference angles to evaluate tan 210 ° .

3 3

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If csc t = 0.68 , what is the csc ( t ) ?

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If cos t = 3 2 , find cos ( t 2 π ) .

3 2

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Which trigonometric functions are even?

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Find the missing angle: cos ( π 6 ) = sin ( ___ )

π 3

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Find the missing sides of the triangle A B C : sin B = 3 4 , c = 12

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Find the missing sides of the triangle.

A right triangle with hyptenuse length of 9 and angle measure of 60 degrees.

a = 9 2 , b = 9 3 2

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The angle of elevation to the top of a building in Chicago is found to be 9 degrees from the ground at a distance of 2000 feet from the base of the building. Using this information, find the height of the building.

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Questions & Answers

A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
Aislinn Reply
cm
tijani
what is titration
John Reply
what is physics
Siyaka Reply
A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
Jude Reply
Can you compute that for me. Ty
Jude
what is the dimension formula of energy?
David Reply
what is viscosity?
David
what is inorganic
emma Reply
what is chemistry
Youesf Reply
what is inorganic
emma
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
Adjei
please, I'm a physics student and I need help in physics
Adjanou
chemistry could also be understood like the sexual attraction/repulsion of the male and female elements. the reaction varies depending on the energy differences of each given gender. + masculine -female.
Pedro
A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
Krampah Reply
2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
Sahid Reply
you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
Samuel Reply
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Joseph Reply
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
Ryan
what's motion
Maurice Reply
what are the types of wave
Maurice
answer
Magreth
progressive wave
Magreth
hello friend how are you
Muhammad Reply
fine, how about you?
Mohammed
hi
Mujahid
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
yasuo Reply
Who can show me the full solution in this problem?
Reofrir Reply
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Practice Key Terms 5

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Source:  OpenStax, Precalculus. OpenStax CNX. Jan 19, 2016 Download for free at https://legacy.cnx.org/content/col11667/1.6
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