Question

What is the value of y?

Triangle A B C has right angle C with hypotenuse labeled 8. Angle A is 60 degrees and its opposite side B C is labeled y.

Enter your answer, as an exact value, in the box.

Answer 1

Answer: y=4√3≈6.93

Explanation:

We know that:

You know that the triangle is a right triangle and you also know the measure of the hypotenuse. Therefore, you must calculate the opposite side y as following:

sin(60°)=opposite/hypotenuse

Where:

opposite=y

hypotenuse=8

Now, when you substitute and solve for the opposite side, you obtain the following result:

y=8*sin(60°)

y=4√3≈6.93

Answer 2

y = 4√3 is the answer.

Explanation:

In the diagram attached we know side AB = 8

Angle A = 60° and side BC = y

We have to find the value of y.

Since sine of angle A = BC/AB = y/8

sin60° = y/8

y = 8sin60°

y = 8×√3/2 = 4√3

Therefore y = 4√3 is the answer.