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elixir [45]
3 years ago
6

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

Mathematics
1 answer:
hram777 [196]3 years ago
5 0

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\°

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