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 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.

Question

48 inches
56 inches
72 inches
131 inches

Answer 1

To determine the height of the painting, we can use basic trigonometric principles. Given the diagonal and the angle, we can use the sine function which relates the angle to the opposite side (height) and the hypotenuse (diagonal).

The formula is:

$$\text{height}=\text{hypotenuse}\times \sin (\text{angle})$$

Where:

• The hypotenuse is the length of the diagonal (86.53 inches).
• The angle is 56.31°.

First, we need to calculate the sine of 56.31°:

$$\sin (56.31°)\approx 0.835$$

Using the formula to find the height:

$$\text{height}=86.53\times \sin (56.31°)\approx 86.53\times 0.835$$ $$\text{height}\approx 72.27\text{ inches}$$

Now, rounding to the nearest inch gives us:

$$\text{height}\approx 72\text{ inches}$$

Thus, the height of the painting is approximately 72 inches.