Download Finding Angles of a Right Triangle

A Follow-Up of Lesson 9-8
Finding Angles of a Right Triangle
A TI-82 calculator can be used to find the measure of an acute angle of a right triangle if
you know the measures of two sides of the triangle.
Example
The end of an exit ramp from an interstate highway is 22 feet higher than the
highway. If the ramp is 630 feet long, what angle does it make with the highway?
630 ft
x˚
22 ft
A
Determine which trigonometric ratio is needed to solve the problem. Since
you know the measure of the leg opposite ⬔A and the hypotenuse, use the
sine ratio.
Write the ratio.
opposite
hypotenuse
sin ⬔A ⫽ ᎏᎏ Sine Ratio
22
630
sin ⬔A ⫽ ᎏᎏ
Substitution
Use a calculator to find the measure of ⬔A. The SIN⫺1 function will find the
angle measure, given the value of its sine.
Be sure that your
2nd [SIN⫺1] ( 22 ⫼ 630 )
ENTER 2.001211869 calculator is in degree
To the nearest degree, the measure of ⬔A is 2°.
mode.
Exercises
Use a calculator to find the measure of each acute angle. Round to the nearest degree.
1.
2.
B
F
E
13.5 ft
7 ft
17 m
A
D
39 m
C
m⬔B ⬇ 59°; m⬔C ⬇ 31°
m⬔F ⬇ 26°; m⬔D ⬇ 64°
3. A flower garden is located 46 meters due west of an elm tree. A fountain is located
19 meters due south of the same elm tree. What are the measures of the angles
formed by these three park features? 22°, 68°, 90°
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482 Chapter 9 Real Numbers and Right Triangles
TI-82