solving right triangles essential question how do i solve a right triangle?
TRANSCRIPT
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