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

Answer:

Part 1) $b=8.2\ units$

Part 2) $a=10.1\ units$

Part 3) $A=51\°$ and $C=90\°$

Step-by-step 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

$A+39\°=90\°$

$A=90\°-39\°$

$A=51\°$