Question

Find the value of X and the value of Y.

A) x=9, y=18 square root 2
B) x=18, y=18
C) x=9 square root 2, y=18 square root 2
D) x=9 square root 3, y=18

Answer 1

D.

Explanation:

Answer 2

Given:

A figure of a triangle.

To find:

The values of x and y.

Solution:

From the given triangle it is clear that the base angles of the triangle are equal, so the triangle is an isosceles triangle.

Altitude on the base of the isosceles triangle from from the opposite angle is a median. It means, it divides the base in two equal parts.

In the given triangle, the altitude divides the base in two equal parts and the measure of each part is 9 units.

In a right triangle,

`\cos \theta=(Base)/(Hypotenuse)`

`\cos 60^circ=(9)/(y)`

`(1)/(2)=(9)/(y)`

`1* y=9* 2`

`y=18`

And,

`\tan \theta=(Perpendicular)/(Base)`

`\tan 60^\circ=(x)/(9)`

`√(3)=(x)/(9)`

`9√(3)=x`

Therefore, the correct option is D.