8.9. Inverse Trigonometric Ratios http://www.ck12.org
In reference to^6 A, we are given theoppositeleg and theadjacentleg. This means we should use thetangentratio.
tanA=^2025 =^45 , therefore tan−^1
( 4
5)
=m^6 A. Use your calculator.If you are using a TI-83 or 84, the keystrokes would be:[ 2 nd][TAN]
( 4
5)
[ENTER]and the screen looks like:So,m^6 A= 38. 7 ◦
Example B
(^6) Ais an acute angle in a right triangle. Use your calculator to findm (^6) Ato the nearest tenth of a degree.
a) sinA= 0. 68
b) cosA= 0. 85
c) tanA= 0. 34
Solutions:
a)m^6 A=sin−^10. 68 = 42. 8 ◦
b)m^6 A=cos−^10. 85 = 31. 8 ◦
c)m^6 A=tan−^10. 34 = 18. 8 ◦
Example C
Solve the right triangle.
To solve this right triangle, we need to findAB,m^6 Candm^6 B. UseACandCBto give the most accurate answers.
AB: Use the Pythagorean Theorem.