Answer:
[tex]B=52.9^o[/tex]
[tex]a=4.041\ mm[/tex]
[tex]b=5.344\ mm[/tex]
Step-by-step explanation:
see the attached figure to better understand the problem
The triangle ABC is a right triangle
we have that
[tex]AB=c=6.7\ mm[/tex]
[tex]AC=b\\BC=a[/tex]
[tex]A=37.1^o[/tex]
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
[tex]cos(A)=\frac{b}{c}[/tex]
substitute the given values
[tex]cos(37.1^o)=\frac{b}{6.7}[/tex]
solve for b
[tex]b=cos(37.1^o)(6.7)[/tex]
[tex]b=5.344\ mm[/tex]
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
[tex]sin(A)=\frac{a}{c}[/tex]
substitute the given values
[tex]sin(37.1^o)=\frac{a}{6.7}[/tex]
solve for a
[tex]a=sin(37.1^o)(6.7)[/tex]
[tex]a=4.041\ mm[/tex]
step 3
Find the measure of angle B
we know that
[tex]A+B=90^o[/tex] ----> by complementary angles
substitute the value of A
[tex]37.1^o+B=90^o[/tex]
[tex]B=90^o-37.1^o[/tex]
[tex]B=52.9^o[/tex]
