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Television sizes are based on the length of the diagonal of the television's rectangular screen. So, for example, a 70-inch television is a television having a diagonal screen length of 70 inches. If a 70 inch television's diagonal forms a 29° angle with the base of the screen, what is the vertical height (h) of the screen to the nearest inch?

Verified Answer :

jmcbutts

the height and width should be h=34.4  w= 61.1

Answer:

34 inches.

Step-by-step explanation:

Length of diagonal AC = 70 inches

A 70 inch television's diagonal forms a 29° angle with the base of the screen i.e.∠ACD = 29°

Now we are supposed to find the vertical height of television.i.e.AB

So, we will use trigonometric ratio:

Using trigonometric ratios  

\(sin\theta = \frac{Perpendicular}{Hypotenuse}\)  

\(sin 29^{\circ} = \frac{AB}{AC}\)  

\(0.484 = \frac{AB}{70}\)  

\(0.484 \times 70=AB\)  

\(33.88=AB\)

Thus the vertical height of the screen to nearest inch is 34 inches.

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