Question

Kendrick is trying to determine if a painting he wants to buy will fit in the space on his wall. If the rectangular frame's diagonal is 50 inches and forms a 36.87° angle with the bottom of the frame, what is its height? Round your answer to the nearest inch. 28 inches 30 inches 38 inches 40 inches

Answer 1

First, draw a diagram to visualize the situation:

Notice that the height of the rectangle is the same as the height of the right triangle formed with the diagonal and the corner of the rectangle.

Since the height is the side opposite to the angle of 36.87º, then, the sine of 36.87º is equal to the ratio of the height h to the hypotenuse 50in:

$\frac{h}{50in}=\sin(36.87º)$

Solve for h:

$h=50in\cdot\sin(36.87º)=30in$

Therefore, the height of the frame is equal to 30 inches.