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Solve the right triangle, ΔABC, for the missing sides and angle to the nearest tenth given angle B = 27° and side c = 15.

User Luhar
by
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2 Answers

2 votes

Answer:

A = 63 , a = 13.4, b = 6.8

Explanation:

User Darme
by
6.5k points
1 vote

Answer:

Part 1)
C=90\°

Part 2)
A=63\°

Part 3)
b=6.8\ units

Part 4)
a=13.4\ units

Explanation:

step 1

Find the measure of angle C

we know that

The triangle ABC is a right triangle

so

Angle C is a right angle

therefore


C=90\°

step 2

Fin the measure of angle A

we know that

In the right triangle ABC

∠B+∠A=90° -----> by complementary angles

we have


B=27\°

substitute


27\°+A=90\°


A=63\°

step 3

Find the length side b

we know that

In the right triangle ABC


sin(B)=b/c


b=(c)sin(B)

substitute the given values


b=(15)sin(27\°)=6.8\ units

step 4

Find the length side a

we know that

In the right triangle ABC


sin(A)=a/c


a=(c)sin(A)

substitute the given values


a=(15)sin(63\°)=13.4\ units

User DoubleDouble
by
6.9k points