8.6. Inverse Trigonometric Ratios http://www.ck12.org
AB: Use the Pythagorean Theorem.
242 +AB^2 = 302
576 +AB^2 = 900
AB^2 = 324
AB=
√
324 = 18
m^6 B: Use the inverse sine ratio.
sinB=24
30
=
4
5
sin−^1(
4
5
)
= 53. 1 ◦=m^6 Bm^6 C: Use the inverse cosine ratio.
cosC=24
30
=
4
5
cos−^1(
4
5
)
= 36. 9 ◦=m^6 CExample 4:Solve the right triangle.
Solution: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. 31BC: Use tangent ratio.
tan 62◦=25
BC
BC=
25
tan 62◦
BC≈ 13. 30