Question

A building lot in a city is shaped as a 30°-60°-90° triangle, like the figure shown.

The side opposite the 30° angle measures 41 feet.




a. Find the length of the side of the lot opposite the 60° angle.
Show how you know.








b. Find the length of the hypotenuse of the triangular lot.
Show how you know.

Answer 1

solution is in photograph

Answer 2

1st part-

Let ABC be the triangle such that

angle A =60°

angle B = 90°

angle C = 30°

Now, AB = 41 feet (opposite to angle C)

Side opposite to angle A = BC

We know,

tan C= AB /BC

tan 30° = 41/BC

BC = 41 root 3 feet

$\sqrt{3}$