To find the height of a tree, a person walks to a point 30 feet from the base of the tree. She measures an angle of
$\mathrm{57\xb0}\text{\hspace{0.17em}}$ between a line of sight to the top of the tree and the ground, as shown in
[link] . Find the height of the tree.
We know that the angle of elevation is
$\text{\hspace{0.17em}}\mathrm{57\xb0}\text{\hspace{0.17em}}$ and the adjacent side is 30 ft long. The opposite side is the unknown height.
The trigonometric function relating the side opposite to an angle and the side adjacent to the angle is the tangent. So we will state our information in terms of the tangent of
$\mathrm{57\xb0},$ letting
$\text{\hspace{0.17em}}h\text{\hspace{0.17em}}$ be the unknown height.
How long a ladder is needed to reach a windowsill 50 feet above the ground if the ladder rests against the building making an angle of
$\text{\hspace{0.17em}}\frac{5\pi}{12}\text{\hspace{0.17em}}$ with the ground? Round to the nearest foot.
We can define trigonometric functions as ratios of the side lengths of a right triangle. See
[link] .
The same side lengths can be used to evaluate the trigonometric functions of either acute angle in a right triangle. See
[link] .
We can evaluate the trigonometric functions of special angles, knowing the side lengths of the triangles in which they occur. See
[link] .
Any two complementary angles could be the two acute angles of a right triangle.
If two angles are complementary, the cofunction identities state that the sine of one equals the cosine of the other and vice versa. See
[link] .
We can use trigonometric functions of an angle to find unknown side lengths.
Select the trigonometric function representing the ratio of the unknown side to the known side. See
[link] .
Right-triangle trigonometry permits the measurement of inaccessible heights and distances.
The unknown height or distance can be found by creating a right triangle in which the unknown height or distance is one of the sides, and another side and angle are known. See
[link] .
Section exercises
Verbal
For the given right triangle, label the adjacent side, opposite side, and hypotenuse for the indicated angle.
A cell phone company offers two plans for minutes. Plan A: $15 per month and $2 for every 300 texts. Plan B: $25 per month and $0.50 for every 100 texts. How many texts would you need to send per month for plan B to save you money?
Hey I am new to precalculus, and wanted clarification please on what sine is as I am floored by the terms in this app? I don't mean to sound stupid but I have only completed up to college algebra.
I don't know if you are looking for a deeper answer or not, but the sine of an angle in a right triangle is the length of the opposite side to the angle in question divided by the length of the hypotenuse of said triangle.
Marco
can you give me sir tips to quickly understand precalculus. Im new too in that topic.
Thanks
Jenica
if you remember sine, cosine, and tangent from geometry, all the relationships are the same but they use x y and r instead (x is adjacent, y is opposite, and r is hypotenuse).
Natalie
it is better to use unit circle than triangle .triangle is only used for acute angles but you can begin with. Download any application named"unit circle" you find in it all you need. unit circle is a circle centred at origine (0;0) with radius r= 1.
SLIMANE
What is domain
johnphilip
the standard equation
of the ellipse that has vertices (0,-4)&(0,4) and foci (0, -15)&(0,15)
it's standard equation is x^2 + y^2/16 =1
tell my why is it only x^2? why is there no a^2?
This term is plural for a focus, it is used for conic sections. For more detail or other math questions. I recommend researching on "Khan academy" or watching "The Organic Chemistry Tutor" YouTube channel.
Chris
how to determine the vertex,focus,directrix and axis of symmetry of the parabola by equations
For each year t, the population of a forest of trees is represented by the function A(t) = 117(1.029)t. In a neighboring forest, the population of the same type of tree is represented by the function B(t) = 86(1.025)t.
It's just like any other number. The important thing to know is that they exist and can be used in computations like any number.
Steve
I would like to add that they are used in AC signal analysis for one thing
Scott
Good call Scott. Also radar signals I believe.
Steve
They are used in any profession where the phase of a waveform has to be accounted for in the calculations. Imagine two electrical signals in a wire that are out of phase by 90°. At some times they will interfere constructively, others destructively. Complex numbers simplify those equations