Question

Solve the right triangle, ΔABC, for the missing sides and angle to the nearest tenth given angle B = 39° and side c = 13.

Answer 1

Part 1)
`b=8.2\ units`

Part 2)
`a=10.1\ units`

Part 3)
`A=51\°` and
`C=90\°`

Explanation:

see the attached figure with letters to better understand the problem

step 1

Find the side b

we know that

In the right triangle ABC

The function sine of angle B is equal to divide the opposite side angle B (AC) by the hypotenuse (AB)

`sin(B)=AC/AB`

we have

`AB=c=13\ units`

`AC=b`

`B=39\°`

substitute

`sin(39\°)=b/13`

solve for b

`b=(13)sin(39\°)`

`b=8.2\ units`

step 2

Find the side a

we know that

In the right triangle ABC

The function cosine of angle B is equal to divide the adjacent side angle B (BC) by the hypotenuse (AB)

`cos(B)=BC/AB`

we have

`AB=c=13\ units`

`BC=a`

`B=39\°`

substitute

`cos(39\°)=a/13`

solve for a

`a=(13)cos(39\°)`

`a=10.1\ units`

step 3

Find the measure of angle A

we know that

In the right triangle ABC

`C=90\°` ----> is a right angle

`B=39\°`

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

substitute the given value

`A+39\°=90\°`

`A=90\°-39\°`

`A=51\°`