CK-12 Geometry Concepts

8.9. Inverse Trigonometric Ratios http://www.ck12.org

Guided Practice

1. Solve the right triangle.


2. Solve the right triangle.

Answers:

1. To solve this right triangle, we need to findAB,BCandm^6 A.

AB: Use sine ratio.

sin 62◦=

25

AB

AB=

25

sin 62◦

AB≈ 28. 31

BC: Use tangent ratio.

tan 62◦=

25

BC

BC=

25

tan 62◦

BC≈ 13. 30

m^6 A: Use Triangle Sum Theorem

62 ◦+ 90 ◦+m^6 A= 180 ◦

m^6 A= 28 ◦

2. Even though, there are no angle measures given, we know that the two acute angles are congruent, making them
   both 45◦. Therefore, this is a 45-45-90 triangle. You can use the trigonometric ratios or the special right triangle
   ratios.

TrigonometricRatios

tan 45◦=

15

BC

sin 45◦=

15

AC

BC=

15

tan 45◦

= 15 AC=

15

sin 45◦

≈ 21. 21

45-45-90TriangleRatios

BC=AB= 15 ,AC= 15

√

2 ≈ 21. 21

Practice

Use your calculator to findm^6 Ato the nearest tenth of a degree.