Question

question 7 of 10
the diagonal of a tv is 26 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. 13 inches by 13√3 inches
b. 13√2 inches by 13√2 inches
c. 52√2 inches by 52√2 inches
d. 52 inches by 52√3 inches

Explanation:

Step1: Recall 30 - 60 - 90 triangle ratios

In a 30 - 60 - 90 triangle, if hypotenuse $c$ is given, the side opposite 30° is $a=\frac{c}{2}$ and side opposite 60° is $b = \frac{c\sqrt{3}}{2}$. Here $c = 26$.

Step2: Calculate side lengths

$a=\frac{26}{2}=13$, $b = 13\sqrt{3}$.

Answer:

A. 13 inches by $13\sqrt{3}$ inches