Question

Solve the triangle ABC if A = 37.1 and c = 6.7 mm. Find B, a, and b. Round a and b to the nearest thousandth as needed.

Answer 1

`B=52.9^o`

`a=4.041\ mm`

`b=5.344\ mm`

Explanation:

see the attached figure to better understand the problem

The triangle ABC is a right triangle

we have that

`AB=c=6.7\ mm`

`AC=b\\BC=a`

`A=37.1^o`

step 1

Find the length side b

The cosine of angle A is equal to divide the adjacent side angle A (side b) by the hypotenuse (side c)

so

`cos(A)=(b)/(c)`

substitute the given values

`cos(37.1^o)=(b)/(6.7)`

solve for b

`b=cos(37.1^o)(6.7)`

`b=5.344\ mm`

step 2

Find the length side a

The sine of angle A is equal to divide the opposite side angle A (side a) by the hypotenuse (side c)

so

`sin(A)=(a)/(c)`

substitute the given values

`sin(37.1^o)=(a)/(6.7)`

solve for a

`a=sin(37.1^o)(6.7)`

`a=4.041\ mm`

step 3

Find the measure of angle B

we know that

`A+B=90^o` ----> by complementary angles

substitute the value of A

`37.1^o+B=90^o`

`B=90^o-37.1^o`

`B=52.9^o`