Solving Right Triangles

Essential Question

How do I solve a right triangle?

Vocabulary

Solve a right triangle – to determine the measures of all six parts (3 angles, 3 sides).

Inverse Trig Ratios

We use the inverse sine, inverse cosine, and inverse tangent if we are trying to find angle measures.

The calculator buttons look like this: sin-1

cos-1

tan-1

Example 1

Find the acute angles of the triangle. Round to the nearest tenth.

C

B

A

13

3

2

tan B = 2

3

mB=tan-1 2

3 mA 90 - 33.7

mA 56.3mB 33.7

Try This!

Find the acute angles of the triangle. Round to the nearest tenth.

34

5

3

F

E

D

mD 31.0

mD =tan-1 3

5

tan D = 3

5

mE 59

mE 90 - 31

Example 2

Solve the right triangle.

sin 25 = h

13

h = 13(sin 25 )

h 5.5

cos 25 = g

13

g = 13(cos 25 )

g 11.8

mG = 90 - 25

mG = 65

13

g

h

25H J

G

Try This!

Solve the right triangle. 15r

s20

S

T R

r 5.1

r = 15(sin 20 )

sin 20 = r

15

s 14.1

s = 15(cos 20 )

cos 20 = s

15

mS = 70

mS = 90 - 20

Summarizer

What is the minimum amount of information needed to solve a right triangle? 2 side lengths or… 1 side length and 1 acute angle measure