1. Right Triangles Trigonometry
Chapter 8.1
Right Triangles Trigonometry

2.  hypotenuse c b leg  leg a
In a right triangle, the shorter sides are called legs and the longest side (which is the one opposite the right angle) is called the hypotenuse 
hypotenuse c b
leg 
leg a

3. Finding angle . 
adjacent h
opposite b c  a

4. Finding angle .  b c
opposite h 
adjacent a

5. Finding the angle from a ratio or decimal value.
If sin 60° = or .8660, then how do we get to turn into 60°?
22.6°
Find ( ) =
We use (.8660) = 60°
Find (1) =
45°
Find (.6587) =
41.2°
Find (- ) =
-53.1°
Find (2.87 ) =
70.8°
Find (.7071) =
45°
Find (2.87 ) =
Error!

6. Example: Solve the triangle. Find a, c, and 
*The sum of the triangle = 180 so,
 = = 50°
40°
adjacent c
Solve for a. Use 40° angle.
b =2
Use tan.
opposite 
=50° a
= 1.68
a = 1.68
Solve for c. Use ????
Pythagorean Theorem
a² + b² = c²
1.68² + 2² = c²
c = 2.61
c = 2.61

7. Example: Solve the triangle. Find c, ,and 
Solve for c. 
a² + b² = c²
3² + 2² = c²
c = 3.61
adjacent c
b =2
opposite
Solve for . Use the given values. 
Use tan.
a = 3
*The sum of the triangle = 180 so,
 = = 33.7°
(3/2) = 56.3°

8. b = 72.79 meters or around 73 meters

9. = 12.7°

10. Angle of Elevation and Angle of Depression

11. b =
Now add the height of the transit = or about 254 meters.

13. A man climbs to the top of a mountain that is 1700 feet tall
A man climbs to the top of a mountain that is 1700 feet tall. He sees the cabin in the valley below at an angle of depression of 37°. How far away is the cabin from the base of the mountain? ?
37°
1700
tan 37° = x
x ~ 2256 ft
1700ft ?