Question

The diagonal of a TV is 30 inches long. Assuming that this diagonal forms a pair of 30-60-90 right triangles, what are the exact length and width of the TV?

A: 15 inches by 15√3 inches
B: 60 inches by 60√3 inches
C: 15√2 inches by 15√2 inches
D: 60√2 inches by 60√2 inches

Answer 1

Your answer is A: 15 inches by 15√3 inches.

We can use trigonometry to solve this. If we draw out one of the triangles we can label the 30 inch side as the hypotenuse, and then the other sides as the opposite and adjacent. Then we just have to find the lengths of these.

To find the opposite, we use the trigonometric ratio sinθ = opposite ÷ hypotenuse, and thus the opposite is sin(60) × 30 = 15√3

Automatically now we know the answer is A because that is the only option with 15√3 as a side, but you could also solve using cosθ = adjacent ÷ hypotenuse and get the other side.

I hope this helps!