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

A = 63 , a = 13.4, b = 6.8

Explanation:

Answer 2

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`