Question

kendrick is trying to determine if a painting he wants to buy will fit in the space on his wall. if the rectangular frames diagonal is 86.53 inches and forms a 56.31° angle with the bottom of the frame, what is its height? round your answer to the nearest inch. (1 point) 48 inches 56 inches 72 inches 131 inches

Explanation:

Step1: Identify trigonometric relation

The height is the side opposite the given angle in a right triangle formed by the diagonal, height, and base of the frame. We use the sine function: $\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$, where $\theta = 56.31^\circ$ and hypotenuse = 86.53 inches.

Step2: Solve for height

Rearrange the formula to isolate height: $\text{Height} = \text{Hypotenuse} \times \sin(\theta)$
Substitute values: $\text{Height} = 86.53 \times \sin(56.31^\circ)$
Calculate $\sin(56.31^\circ) \approx 0.832$, so $\text{Height} \approx 86.53 \times 0.832 \approx 72$

Answer:

72 inches