Answer:
Height is 35.3 inches.
Width is 62.8 inches.
Dimensions are 62.8 by 35.3.
Step-by-step explanation:
We can solve this problem using some simple trigonometry.
First, we need to calculate the angle of the corner to corner line relative to the base. We use tan⁻¹ to solve for this.
tan⁻¹([tex]\frac{9}{16}[/tex])
29.35775354°
We can now use this angle to find the side length to hypotenuse ratios. First, we will find the height using sine.
sin is [tex]\frac{opposite}{hypotenuse}[/tex]
[tex]\frac{x}{72}[/tex] = sin(29.35775354°) --- plug in known info
[tex]\frac{x}{72}[/tex] = 0.4902612396 --- solve
x = 0.4902612396 × 72 --- multiply both sides by 72
x = 35.29880925
Height is 35.3 inches.
Now, we can solve for the width using cosine.
cos is [tex]\frac{adjacent}{hypotenuse}[/tex]
[tex]\frac{w}{72}[/tex] = cos(29.35775354°) --- plug in known info
[tex]\frac{w}{72}[/tex] = 0.8715755371 --- solve
w = 0.8715755371 × 72 --- multiply both sides by 72
w = 62.75343867
w = 62.8 inches
