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vova2212 [387]
3 years ago
10

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

Mathematics
1 answer:
sertanlavr [38]3 years ago
6 0

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

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