Question

A TV is measured diagonally. In the 30 - 60 - 90 triangle, the diagonal measures 24√3 inches long. What is the length of the TV?

Answer 1

To be able to determine the length of the TV, let's focus only on one of the triangles that is formed.

Where,

x = the length of the TV.

To find x, we will be applying the Cosine Function:

`\text{ Cosine }\theta\text{ = }\frac{Adjacent\text{ Side}}{\text{Hypotenuse}}`
`Cosine(30^(\circ))\text{ = }\frac{x}{\text{2}4\sqrt[]{3}}`
`\text{ 24}\sqrt[]{3}xCosine(30^(\circ))\text{ = x}`
`(24\sqrt[]{3})(\frac{\sqrt[]{3}}{2})\text{ = x}`
`\text{ }\frac{24\text{ x 3}}{2}\text{ = x}`
`\text{ }(72)/(2)\text{ = x}`
`\text{ 36 inches = x}`

Therefore, the length of the TV is 36 inches.