Download Trigonometry 3 - Finding Angles

Math 10C
Trigonometry Lesson #3
Using Trigonometric Ratios to Find Angles
Objective: By the end of this lesson you will be able to:
Recall: The tangent, sine, and cosine ratios for a given angle are always the same, regardless of
the size of the triangle.
We have used our calculator to solve for a trig ratio when given the angle. We can also work the
other way, and find the angle if we are given a trig ratio. This requires using the 2nd function of
the sin, cos, and tan buttons:
e.g. 1) Use your calculator to find the angles for each trig ratio, to the nearest degree.
*Remember to make sure your calculator is in _____________ mode!
b) tan V 
a) sin A  0.85
2
7
c) cos  0.7071
We can use this process to find missing angles in a right triangle if we know the lengths of at
least two sides.
1. Label the sides of the triangle with respect to the angle you are trying to find:
2. Choose which trig ratio to use based on the sides you are given.
* Use _______________________
3. Set up the trig ratio: The variable will be the ____________.
4. Use ___________________________ on your calculator to solve for the angle.
e.g. 2) Find the measure of J , to the nearest tenth of a degree.
H
4 cm
K
9 cm
J
Math 10C
Trigonometry Lesson #3
e.g. 3) A support cable is anchored to the ground 5 m from the base of a telephone pole. The
cable is 19 m long. What angle, to the nearest degree, does the cable make with the
ground?
Terminology:
 Angle of elevation (or angle of inclination):

Angle of depression:
Most Important Point:
e.g. 4) In the diagram below, label the angle of elevation from A to B and the angle of depression
from B to A. What is the relationship between the angle of elevation and the angle of
depression?
B
A
Math 10C
Trigonometry Lesson #3
e.g. 5) A cruise ship is anchored at sea 1.1 km from the base of a 73-m high cliff. What is the
angle of depression, to the nearest tenth of a degree, from the top of the cliff to the cruise
ship?
Assignment:
p. 75-77 #4, 5, 8, 10, 11, 14, 17-19
p. 95-96 #6-8, 10-13