Question

Which of the following options accurately represents the exact length and width of the TV, assuming that its diagonal, forming a pair of 30-60-90 right triangles, measures 30 inches?

A. 15.2 inches by 15.12 inches
B. 60 inches by 60/3 inches
C. 15 inches by 15/3 inches
D. 60/2 inches by 600/2 inches

Answer 1

The exact length and width of the TV, assuming a 30-60-90 right triangle, would be 15 inches by 15√3 inches.

Step-by-step explanation:

To find the exact length and width of the TV, we will use the 30-60-90 right triangles formed by the diagonal. In a 30-60-90 triangle, the ratio of the shorter leg to the hypotenuse is 1:2, and the ratio of the longer leg to the hypotenuse is √3:2. Since the diagonal of the TV measures 30 inches, the shorter leg would be 15 inches (30/2) and the longer leg would be 15√3 inches (30√3/2). Therefore, the exact length and width of the TV would be 15 inches by 15√3 inches.