1. Do Now

2. Objective: To use inverse sine, cosine and tangent.
7.7 Solve Right Triangles
Objective: To use inverse sine, cosine and tangent.

3. Solve a Right Triangle:
Find the measures of all the sides and angles.
You need to know either…
Two side lengths or
One side length and the measure of one acute angle.

4. Inverse Trigometric RatiosB
Let A be an acute angle. Ð C A
Inverse Tangent: If tan A = x, then tan-1 x = m A. Ð
Inverse Sine: If sin A = y, then sin-1 y = m A. Ð
Inverse Cosine: If cos A = z, then cos-1 z = m A. Ð

5. Ð Ð Ð Examples tan-1 = m A sin-1 = m A tan-1 = m A tan-1 1.5 = 56.3

6. Examples (cont.) m U = 20o Tan-1 = m P m P = 45o 54.8 = m P
m N = 90 – 54.8
m N = 35.2
14.1 = UT
a2 + b2 = c2
a2 =
8.49 = PQ
= c2
a2 = 26.19
= c2
8.49 = QR
a = 5.1
433 = c2
c = 20.8