# The size of a tv is determined by the length of the diagonal of the TV. A 42” tv means the length from one corner to the other

The size of a tv is determined by the length of the diagonal of the TV. A 42” tv means the length from one corner to the other is 42”. If the diagonal forms a 30 degree angle with the base of the TV what are the height and width of the TV

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1. butterflycc says:

height of TV = 21"

Width of TV = 36.372"

Step-by-step explanation:

The TV is rectangular and the diagonal divides the rectangle into 2 equal right angle triangles. The diagonal represents the hypotenuse of the right angle triangle. If the diagonal forms a 30 degree angle with the base of the TV, then the height of the TV represents the opposite side of the right angle triangle and the width of the TV represents the adjacent side of the right angle triangle.

To determine the height, h of the TV, we would apply the Sine trigonometric ratio.

Sin θ = opposite side/hypotenuse. Therefore,

Sin 30 = h/42

h = 42Sin30 = = 42 × 0.5

h = 21"

To determine the width, w of the TV, we would apply the

the cosine trigonometric ratio.

Cos θ, = adjacent side/hypotenuse. Therefore,

Cos 30 = w/42

w = 42Cos30 = 42 × 0.866

w = 36.372"