Question

question 4 of 10
the diagonal of a tv is 28 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. ( 14sqrt{2} ) inches by ( 14sqrt{2} ) inches
b. 14 inches by ( 14sqrt{3} ) inches
c. 56 inches by ( 56sqrt{3} ) inches
d. ( 56sqrt{2} ) inches by ( 56sqrt{2} ) inches

Explanation:

Step1: Recall 30-60-90 triangle ratios

In a 30-60-90 right triangle, the sides are in the ratio \(1 : \sqrt{3} : 2\), where the side opposite 30° is the shortest (\(x\)), opposite 60° is \(x\sqrt{3}\), and the hypotenuse is \(2x\).

Step2: Identify hypotenuse and solve for \(x\)

The diagonal of the TV is the hypotenuse of the 30-60-90 triangle, so \(2x = 28\). Solving for \(x\): \(x=\frac{28}{2}=14\).

Step3: Find the other side

The other side (opposite 60°) is \(x\sqrt{3}=14\sqrt{3}\). So the length and width of the TV (the legs of the right triangle) are 14 inches and \(14\sqrt{3}\) inches.

Answer:

B. 14 inches by \(14\sqrt{3}\) inches