1 What you will learn  How to evaluate inverse trigonometric functions  How to find missing angle measures  How to solve right triangles

Objective: Section 5-5 Solving Right Triangles 2 Introduction Sometimes when solving triangles, we know the trigonometric value of an angle but not the angle. When solving these problems, we need to use the inverse of a trigonometric function (working backward from the ratio to the angle measure).

Objective: Section 5-5 Solving Right Triangles 3 Definitions The inverse of the basic trigonometric functions: Arcsine = inverse of sine (sin -1 ) Arccosine = inverse of cosine (cos -1 ) Arctangent = inverse of tangent (tan -1 )

Objective: Section 5-5 Solving Right Triangles 4 Example sin x = can be re-written as x = arcsin The answer consists of all angles that have as the value of sine x.

Objective: Section 5-5 Solving Right Triangles 5 Example Problems  Solve each equation. A. Sin x = C. Tan x = 1 B. Cos x =

Objective: Section 5-5 Solving Right Triangles 6 More Examples  Evaluate each expression. Assume all angles are in Quadrant I. A. B.

Objective: Section 5-5 Solving Right Triangles 7 You Try  Evaluate each expression. Assume that all angles are in Quadrant I. A. B.

Objective: Section 5-5 Solving Right Triangles 8 Finding Angle Measures  If f = 17 and d = 32, find E.  You Try! If d = 28 and f = 21, find F. F D E f e d

Objective: Section 5-5 Solving Right Triangles 9 Word Problem  A security light is being installed outside a loading dock. The light is mounted 20 feet above the ground. The light must be placed at an angle so that it will illuminate the end of the parking lot 100 feet away. What should the angle of depression be?

Objective: Section 5-5 Solving Right Triangles 10 Solving Right Triangles  Solve the triangle described. A. A = 33 o, b = 5.8 B. a = 23, c = 45 A B C a b c

Objective: Section 5-5 Solving Right Triangles 11 You Try  Solve each triangle described. Round to the nearest tenth. A. K = 40 o, k = 26 B. j = 65, l = 55 K J L j l k

Objective: Section 5-5 Solving Right Triangles 12 Homework Homework: page 309, even, even, even, 44