Algebra 1 Common Core Student Edition, Grade 8-9

You can use trigonom etry to find m issing lengths in a right triangle w h en you know the

length of one side an d th e m easu re of a n acute angle.

How can you find the
measure of the third
angle of the triangle?
The sum of the measures
of the angles of a
triangle is 180°. You can
subtract the measures of
the two known angles
from 180° to find the
third angle's measure.

Problem 3 Finding a Missing Side Length

To the nearest tenth, what is the value of x in the triangle at the right?

• The measure of an
  acute angle


• The length of the
  hypotenuse

The length of the

opposite leg

Jg lfla -_____

Use the sine ratio.

Write an equation an d solve.

sin 48° =

0 _ opposite leg

hypotenuse

sin 48° = ft

x = 14(sin 48°)

Use the definition o f sine.

Substitute x and 14 from the diagram.

Solve fo r x.

x ~ 10.40402756 Use a calculator.

x ~ 10.4 Round to the nearest tenth.

The value of x is ab o u t 10.4.

G o t It? 3. To th e n ea rest tenth, w h at is th e value of x in th e triangle at th e right? 1.575

If you know th e lengths of two sides of a right triangle, you can find a trigonom etric ratio

for each acute angle of th e triangle. If you know a trigonom etric ratio for a n angle, you

can use th e inverse of th e trigonom etric ratio to find th e m easure of th e angle. Use the

sin-1 , cos-1 , or tan-1 feature o n your calculator.

Finding the M easures of Angles

What is the measure of each angle in the triangle at the right?

Step 1 Since you know th e length of th e side adjacent to LA a n d th e length

of th e hypotenuse, use th e cosine ratio.

Step 2 Write a n eq u a tio n an d solve.

cos A =

cos A = 0.5

measure of LA = cos-1 (0.5)

m easu re of LA = 60°

Use the definition o f cosine.

Divide.

Use the inverse o f cosine.

Use a calculator.

LA m easures 60°. The right angle B m easu res 90°. LC m easures

180° - 90° - 60° = 30°.

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