1. SOLVING RIGHT TRIANGLES
Pythagorean Theorem:
a2 + b2 = c2 where a & b are legs of a
right triangle & c is the hypotenuse B c a A C b

2. Recall:
SIN
COS
TAN O O A H A H
CSC
SEC
COT
“Solve the right triangle” means find all of the sides and angles.

3. When solving for x, this is NOT what is means:

4. Note: 39˚12‘ means 39 degrees 12 minutes (12/60 of a degree).
Ex. Solve the right triangle given that A=39˚12‘ and b=2.1. B
A= a=
B= b=
C= c=
39˚12‘
1.7 c
50˚48‘ a
2.1
39˚12‘ A
90˚
2.7 C b
=2.1
Need: a, c, B
B= 90˚-39˚12‘
B=50˚48‘
tan A = O/A
tan 39˚12‘= a/2.1
.8156=a/2.1
a = 1.7
cos A = A/H
cos 39˚12‘= 2.1/c
c=2.1/cos 39˚12‘
c = 2.7

5. Ex. Solve the right triangle given that a=2 and b=7.
Note: 50.8˚ means 50 degrees 8/10 of a minute (or .8•60)=48 min.=50˚48‘
Ex. Solve the right triangle given that a=2 and b=7. B
A= a=
B= b=
C= c=
16˚ 2 c
74˚
a=2 7 A
90˚
7.3 C b =7
Need: c, A, B
Pythag =c2
c2=53
c = 7.3
tan A = O/A
tan A= 2/7
A=tan-1(2/7)
A = 15.9 or 16˚
B=90-16
B = 74˚