Question

Find the missing sides of the triangle. Leave youranswers as simplified radicals.

Answer 1

Step-by-step explanation:

Consider the following right triangle:

To find the missing sides x and y, we can apply the following trigonometric ratios:

`\cos(60^(\circ))=\frac{adjacent\text{ side to the angle 60}^(\circ)}{Hypotenuse}`

`\sin(60^(\circ))=\frac{opposite\text{ side to the angle 60}^(\circ)}{Hypotenuse}`

and

`\tan(60^(\circ))=\frac{opposite\text{ side to the angle 60}^(\circ)}{adjacent\text{ side to the angle 60}^(\circ)}`

thus, applying the data of the problem to the last equation, we get:

`\tan(60^(\circ))=\frac{opposite\text{ side to the angle 60}^(\circ)}{adjacent\text{ side to the angle 60}^(\circ)}=(15)/(y)`

that is:

`\tan(60^(\circ))=(15)/(y)`

solving for y, we obtain:

`y=(15)/(\tan(60^(\circ)))=(15)/(√(3))`

On the other hand, applying the above data to the first equation, we get:

`\cos(60^(\circ))=\frac{adjacent\text{ side to the angle 60}^(\circ)}{Hypotenuse}=(y)/(x)=(15)/(√(3))\text{ }\cdot(1)/(x)`

or

`\cos(60^(\circ))=\frac{15}{√(3)\text{ x}}\text{ }`

solving for x, we obtain:

`x=(15)/(√(3)\cdot\cos(60))=\text{ }\frac{15}{\sqrt{3\text{ }}\cdot1/2}=(2(15))/(√(3))=(30)/(√(3))`

we can conclude that the correct answer is:

Answer:

`x=(30)/(√(3))`

and

`y=(15)/(√(3))`