The length of the hypotenuse of a 30°-60°-90° triangle is 8. What is the length of the longer leg? Enter your answer as an exact number (not rounded).

The length of the longer leg is 6.928

Explanation:

The 30°-60°-90° triangle given is a right angled triangle. A right angled triangle is made up or 2 sides namely the adjacent, the opposite and the hypotenuse. The longest of all this three sides is the hypotenuse.

Given the length of the hypotenuse to be 8.

Note that the long leg is different from the longest side. The long leg is always the length opposite the 60° angle while the short leg is the side opposite the 30° angle.

Using SOH CAH TOA to solve for the long leg we have;

Sin (theta) = Opposite/Hypotenuse

Theta = 60° (angle directly opposite the long leg)

Opposite = length of the long leg

Hypotenuse is the longest side = 8

Substituting this value in the formula we will have;

Sin60° = opposite/8

Opposite = 8sin60°

Opposite = 6.928

This means that the length of the longer leg is 6.928.