Geometry Warm-Up

Solve for the missing side (Solve for x):

Set up ratio, last step, plug into calculator

52°

32

x

33°

8 x

13°

x 11

12.2 Problem Solving with Right Triangles

1. Right triangle trig is often used to indirectly find the height of a tall object.

2. For each problem you must draw a picture!!!

Step 1: draw and label a pictureStep 2: set up your proportionStep 3: Solve and label your answer

26ft

33.5o

x x

265.33sin

Example 1:

A water slide is 26 feet high. The angle between the slide and the water is 33.5°.

What is the length of the slide?

26

sin 33.5x

x = 47.1 feet

Angle of Depression and Elevation

If you look up, you measure the angle of elevation

If you look down you measure the angle of depression

The angle of depression and elevation are congruent

Example 2: The angle of elevation from a sailboat to the top

of lighthouse on shore is 16o. If the sailboat is 422 ft from shore, how tall is the lighthouse?

422 tan16 x

x

16o

422 ft

Set up a proportion:

42216tan

x

x = 121 ft

Example 3: The angle of depression is 8o from a watch

tower to a forest fire if the watch tower is 25 m high, what is the distance between

the base of the tower and the fire?

25m

x m

Where is the angle of depression?

25tan8

25

tan8

x

x

8o

8o

Here it is!

x = 177.9 m

Summary:

What information do you need in order to solve a right triangle word problem?