Question

What are the dimensions of a 72in television with a 16:9 aspect ratio

Answer 1

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($\frac{9}{16}$)

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 $\frac{opposite}{hypotenuse}$

$\frac{x}{72}$ = sin(29.35775354°) --- plug in known info

$\frac{x}{72}$ = 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 $\frac{adjacent}{hypotenuse}$

$\frac{w}{72}$ = cos(29.35775354°) --- plug in known info

$\frac{w}{72}$ = 0.8715755371 --- solve

w =  0.8715755371 × 72 --- multiply both sides by 72

w = 62.75343867

w = 62.8 inches