Warm up• 1. Use the unit circle to find each value:

– a. cos (-180o)– b. tan(45o)

• 2. Find the values of the six trig functions for angle in standard position if a point with coordinates (6, -5) lies on its terminal side.

Lesson 5-4 Applying Trig Functions

Objective: To use the 6 trig functions to find the measures of the sides of right triangles.

Solving a Triangle• USE YOUR CALCULATOR

• Set Mode to degree

Solving a Right Triangle• If you know the angle but only one side you

can find the other dimensions.

• cos 60 = 3 cUse calculator: cos 60 = .5.5 = 3 cC = 6

ca

3 AC

β

60o

B

Try• In a triangle ABC, α = 64o, γ = 90o, and b =

24.7• Solve the triangle.

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eye - levelThe angles are equal – they are alternate angles

Practice• An observer in the top of a lighthouse

determines that the angles of depression to two sailboats directly in line with the lighthouse are 3.5o and 5.75o. If the observer is 125 feet above sea level, find the distance between the boats.

Practice• A regular hexagon is inscribed in a circle

with a diameter 26.6 centimeters. Find the apothem of the hexagon.