Question

What are the missing angle measures in triangle ABC?

Answer 1

we know that

In the right triangle ABC

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

so

Step $1$

Find the measure of angle B

we know that

$tan\ B=\frac{opposite\ side\ angle\ B}{adjacent\ side\ angle\ B}$

in this problem

$opposite\ side\ angle\ B=7in\\ adjacent\ side\ angle\ B=5in$

so

$tan\ B=\frac{7}{5} \\ \\ B=arc\ tan\frac{7}{5} \\ \\ B=54.5\ degrees$

Step $2$

Find the measure of angle A

$A+B=90\\ A=90-B\\ A=90-54.5\\ A=35.5\ degrees$

therefore

the answer is the option

35.5° and 54.5°

Answer 2

35.5° and 54.5°

solve though tangent