Question

30°-60°-90°
Find the missing sides of the triangle.

Answer 1

Explanation:

30+-60+-90=?

30+60=90

Answer 2

In a 30°-60°-90° triangle, the side opposite the 30° angle is half the length of the hypotenuse, and the side opposite the 60° angle is √3 times smaller than the hypotenuse.

Let x be the length of the hypotenuse, then the side opposite the 60° angle is 6√3. Therefore, we have:

x/2 = 6√3/√3

Simplifying the right side, we get:

x/2 = 6

Multiplying both sides by 2, we get:

x = 12

So the length of the hypotenuse is 12.

To find the length of the side opposite the 30° angle, we use the fact that it is half the length of the hypotenuse:

x/2 = 12/2 = 6

So the length of the side opposite the 30° angle is 6.