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. 60 inches by 60\sqrt{3} inches
b. 60\sqrt{2} inches by 60\sqrt{2} inches
c. 15\sqrt{2} inches by 15\sqrt{2} inches
d. 15 inches by 15\sqrt{3} inches

Explanation:

Step1: Recall 30 - 60 - 90 triangle ratio

In a 30 - 60 - 90 right - triangle, the side lengths are in the ratio $1:\sqrt{3}:2$. Let the shorter leg be $x$, the longer leg be $x\sqrt{3}$, and the hypotenuse be $2x$.

Step2: Find the value of $x$

The diagonal of the TV is the hypotenuse of the right - triangle, and it is given as 30 inches. So, $2x = 30$, which gives $x=\frac{30}{2}=15$ inches.

Step3: Determine the length and width

The shorter side (width) of the TV is the shorter leg of the 30 - 60 - 90 triangle, which is $x = 15$ inches. The longer side (length) of the TV is the longer leg of the 30 - 60 - 90 triangle, which is $x\sqrt{3}=15\sqrt{3}$ inches.

Answer:

D. 15 inches by $15\sqrt{3}$ inches