Question

question 6 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. 56√2 inches by 56√2 inches
b. 56 inches by 56√3 inches
c. 14√2 inches by 14√2 inches
d. 14 inches by 14√3 inches

Explanation:

Step1: Recall 30-60-90 triangle ratio

Sides ratio: \(1 : \sqrt{3} : 2\) (opposite 30°, 60°, 90°)

Step2: Hypotenuse equals TV diagonal

Hypotenuse = 28 inches = \(2x\) → \(x = 14\)

Step3: Calculate legs

Short leg: \(x = 14\) inches; Long leg: \(x\sqrt{3} = 14\sqrt{3}\) inches

Answer:

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