Question

Given the following information, find the length of the missing side. Leave your answer as a simplified radical. Long = 3, Hypotenuse = ?

1) 2
2) 2√3
3) 3√3
4) 6

Answer 1

The length of the missing side (Hypotenuse) is 6, which corresponds to 6. Option (4) is true.

Explanation:

To find the length of the missing side (Hypotenuse) in a right-angled triangle given the lengths of the other two sides, we can use the trigonometric relationship of the sides of a 30-60-90 triangle.

In a 30-60-90 right-angled triangle, if the length of the shorter leg (opposite the 30-degree angle) is (a), then the length of the hypotenuse is (2a).

Given:

Long leg = 3

We need to find the length of the hypotenuse.

Using the relationship in a 30-60-90 triangle, the length of the hypotenuse is twice the length of the long leg.

So,

Hypotenuse = 2 x 3

= 6

Therefore, Option (4) is true.