Question

Could you explain the following problem:A tunnel is to be dug from point A to point B. Both A and B are visible from point C. If AC is 250 miles and BC is 526 miles, and if angle C is 90°, find the measure of angle B. Round to tenths place.

Answer 1

Okay, here we have this:

Considering the provided information, we are going to graph the situation and find the requested angle, so we obtain the following:

We want to know the measure of angle B, and we know the measure of its adjacent leg and opposite leg, since the triangle is a rectangle, then we can use the tangent ratio, so we have this:

$\begin{gathered} \tan (B)=\frac{250}{526} \\ B=\arctan \mleft(\frac{125}{263}\mright) \\ B\approx25.4\text{ degre}es \end{gathered}$

Finally we obtain that the measure of angle B is approximately 25.4°.