Question

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

Answer 1

Answer:

Part 1) $C=90\°$

Part 2) $A=63\°$

Part 3) $b=6.8\ units$

Part 4) $a=13.4\ units$

Step-by-step 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

$a=(15)sin(63\°)=13.4\ units$