Question

50 POINTS! What is the value of x?

4

4√3

8

​ 8√3 ​
The figure contains a right triangle. The side opposite the right angle is 8. The side opposite the 60 degree angle is x.

Answer 1

`4√(3)`

Explanation:

Since the triangle is a right triangle with a 60 degree angle, the triangle is what can be referred to as a 30-60-90 triangle. In this type of triangle, the larger leg (the one opposite the 60 degree angle) is
`√(3)` times larger than the smaller leg (the one opposite the 30 degree angle). Also, the hypotenuse (the side opposite the right angle) is twice larger than the smaller leg. Since the smaller leg is 8/2=4 units long, x is
`√(3)` larger than that or just
`4√(3)`. Hope this helps!

Answer 2

4√3

Explanation:

We can use trig functions since this is a right triangle

The side opposite the right angle is 8, that is the hypotenuse

We know the opposite side is x

sin theta = opp/ hyp

sin 60 = x/8

Multiply each side by 8

8 sin 60 =x

sin 60 = sqrt(3)/2

8 (sqrt(3)/2 =x

4 sqrt(3) =x