Question

Question 8 of 10The diagonal of a TV is 30 inches long. Assuming that this diagonal forms apair of 30-60-90 right triangles, what are the exact length and width of the TV?A. 60 inches by 60/3 inchesB. 15 inches by 15/5 inchesC. 60/2 inches by 600/2 inchesO D. 15.2 inches by 15.2 inches

Answer 1

The diagram of the triangle formed is shown below

The length is BC and the width is AB

To find BC, we would apply the cosine trigonometric ratio which is expressed as

Cos# = adjacent side /hypotenuse

hypotenuse = AC = 30

adjacent side = BC

# = 30

Thus, we have

`\begin{gathered} \text{Cos}30\text{ = }(BC)/(30) \\ \text{Note, Cos30 = }\frac{\sqrt[]{3}}{2} \\ We\text{ have} \\ \frac{\sqrt[]{3}}{2}=\text{ }(BC)/(30) \\ 2BC\text{ = 30}\sqrt[]{3} \\ BC\text{ = }\frac{30\sqrt[]{3}}{2} \\ BC\text{ = 15}\sqrt[]{3} \end{gathered}`

To find AB, we would apply the sine trigonometric ratio which is expressed as

Sin# = opposite side /hypotenuse

hypotenuse = AC = 30

opposite side = AB

# = 30

Thus, we have

Sin30 = AB/30

Recall, sin30 = 0.5

Thus,

0.5 = AB/30

AB = 30 * 0,5

AB = 15

Thus, the correct option is B