How many “parts” are in every triangle?
Six  3 angles and 3 sides
If we have any three of these parts, we can usually find the other three…
This process is called solving a triangle.

Solving Right Triangles
A right triangle with a hypotenuse of 8 includes a 37 degree angle. Find the measures of all of the other parts of the triangle.
First, the missing angle:
Start with a diagram:
37
8 b b
180 – 90 – 37 = 53
  b sin 37
Use trig. to find the other sides:

4.815
a

6.389
a
8 a b

8sin 37
 a

8cos37


Solving Right Triangles a
B
Use the given information to completely solve the triangle.
  
10
 c
 c
C
 b a

6.561
A b

7.547
 
49


Solving Right Triangles a
Use the given information to completely solve the triangle.
B a

5
  
 c
C
 b b

8.321
A c

9.708
  

Solving Right Triangles h
From a point 340 feet away from the base of Peachtree Center
Plaza in Atlanta, GA, the angle of elevation to the top of the building is 65 . Find the height h of the building.
The diagram?
65
340 ft tan 65
  h h

340
340 tan 65
 h

729.132
feet

Whiteboard Problems
Kirsten places her surveyor’s telescope on the top of a tripod 5 ft above the ground. She measures an 8 degree elevation above the horizontal to the top of a tree that is 120 ft away. How tall is the tree?
h

21.865
feet

Whiteboard Problems
A climber falls from the top of a cliff and is stuck on a ledge some distance off the ground. A rescue party is currently 1200 ft from the base of the cliff, and spots the climber and the top of the cliff at angles of 55 and 62 , respectively. How far did the climber fall?
d

543.094
feet