Transcript Solving Right Triangles

Warm – up

Find the sine, cosine and tangent of angle c.
B
C
15
A
Solving Right
Triangles
Section 5.4
Standards

MM2G2. Students will define and apply sine,
cosine, and tangent ratios to right triangles.



Discover the relationship of the trigonometric
ratios for similar triangles.
Explain the relationship between the trigonometric
ratios of complementary angles.
Solve application problems using the
trigonometric ratios.
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.

B
3
C
2
tan B =
3
m
B=tan-1

2
3
mB  33.7
13
2
mA  90 - 33.7
A
mA  56.3
Try This!

Find the acute angles of the triangle. Round to the
nearest tenth.
E
34
3
tan D =
5
mD
=tan-1
3
D

3
5
mD  31.0
5
mE  90 - 31
mE  59
F
Example 2

Solve the right triangle.
h
sin 25 =
13
h = 13(sin 25)
g
cos 25 =
13
g = 13(cos 25)
h  5.5
g  11.8
mG = 90 - 25
mG = 65
H
g
25
13
J
h
G
Try This!
S

Solve the right triangle.
r
sin 20 =
15
s
cos 20 =
15
r = 15(sin 20)
s = 15(cos 20)
r  5.1
s  14.1
mS = 90 - 20
mS = 70
r
T
15
s
20
R
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
Homework

Pages 174 – 175

Numbers 2 – 26 even