Question

Solve for an angle in right triangles

I just need the answer i don’t need the whole thing explained :)

Answer 1

`m \angle B \approx 64.62 \textdegree`

Explanation:

First find, the length of side AC using the Pythagorean Theorem.

`3^2 + AC^2 = 7^2`

`9 + AC^2 = 49`

`AC^2 = 40`

`AC = √(40)`

`AC = 2√(10)`

Then, use the trigonometric ratio tangent to solve for m∠B.

`\tan(m\angle B) = (2√(10))/(3)`

`m\angle B = \tan^(-1)\left((2√(10))/(3)\right)`

`m \angle B \approx 64.62 \textdegree`