7.2 Right triangle trigonometry  (Page 5/12)

 Page 5 / 12

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.

About 52 ft

Access these online resources for additional instruction and practice with right triangle trigonometry.

Key equations

 Trigonometric Functions Reciprocal Trigonometric Functions Cofunction Identities

Key concepts

• 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 facilitates 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] .

Verbal

For the given right triangle, label the adjacent side, opposite side, and hypotenuse for the indicated angle.

When a right triangle with a hypotenuse of 1 is placed in a circle of radius 1, which sides of the triangle correspond to the x - and y -coordinates?

The tangent of an angle compares which sides of the right triangle?

The tangent of an angle is the ratio of the opposite side to the adjacent side.

What is the relationship between the two acute angles in a right triangle?

Explain the cofunction identity.

For example, the sine of an angle is equal to the cosine of its complement; the cosine of an angle is equal to the sine of its complement.

Algebraic

For the following exercises, use cofunctions of complementary angles.

$\mathrm{cos}\left(34°\right)=\mathrm{sin}\left(___°\right)$

$\mathrm{cos}\left(\frac{\pi }{3}\right)=\mathrm{sin}\left(___\right)$

$\frac{\pi }{6}$

$\mathrm{csc}\left(21°\right)=\mathrm{sec}\left(___°\right)$

$\mathrm{tan}\left(\frac{\pi }{4}\right)=\mathrm{cot}\left(___\right)$

$\frac{\pi }{4}$

For the following exercises, find the lengths of the missing sides if side $\text{\hspace{0.17em}}a\text{\hspace{0.17em}}$ is opposite angle $\text{\hspace{0.17em}}A,$ side $\text{\hspace{0.17em}}b\text{\hspace{0.17em}}$ is opposite angle $\text{\hspace{0.17em}}B,$ and side $\text{\hspace{0.17em}}c\text{\hspace{0.17em}}$ is the hypotenuse.

$\mathrm{cos}\text{\hspace{0.17em}}B=\frac{4}{5},a=10$

$\mathrm{sin}\text{\hspace{0.17em}}B=\frac{1}{2},a=20$

$b=\frac{20\sqrt{3}}{3},c=\frac{40\sqrt{3}}{3}$

$\mathrm{tan}\text{\hspace{0.17em}}A=\frac{5}{12},b=6$

$\mathrm{tan}\text{\hspace{0.17em}}A=100,b=100$

$a=10,000,c=10,00.5$

Questions & Answers

the gradient function of a curve is 2x+4 and the curve passes through point (1,4) find the equation of the curve
Kc Reply
1+cos²A/cos²A=2cosec²A-1
Ramesh Reply
test for convergence the series 1+x/2+2!/9x3
success Reply
a man walks up 200 meters along a straight road whose inclination is 30 degree.How high above the starting level is he?
Lhorren Reply
100 meters
Kuldeep
Find that number sum and product of all the divisors of 360
jancy Reply
answer
Ajith
exponential series
Naveen
what is subgroup
Purshotam Reply
Prove that: (2cos&+1)(2cos&-1)(2cos2&-1)=2cos4&+1
Macmillan Reply
e power cos hyperbolic (x+iy)
Vinay Reply
10y
Michael
tan hyperbolic inverse (x+iy)=alpha +i bita
Payal Reply
prove that cos(π/6-a)*cos(π/3+b)-sin(π/6-a)*sin(π/3+b)=sin(a-b)
Tejas Reply
why {2kπ} union {kπ}={kπ}?
Huy Reply
why is {2kπ} union {kπ}={kπ}? when k belong to integer
Huy
if 9 sin theta + 40 cos theta = 41,prove that:41 cos theta = 41
Trilochan Reply
what is complex numbers
Ayushi Reply
Please you teach
Dua
Yes
ahmed
Thank you
Dua
give me treganamentry question
Anshuman Reply
Solve 2cos x + 3sin x = 0.5
shobana Reply

Read also:

Get the best Algebra and trigonometry course in your pocket!

Source:  OpenStax, Algebra and trigonometry. OpenStax CNX. Nov 14, 2016 Download for free at https://legacy.cnx.org/content/col11758/1.6
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Algebra and trigonometry' conversation and receive update notifications?

 By By By