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.

the correct choice is a .

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the order for strong to weak forces such as

strong nuclear force → electromegnetic force → weak nuclear force → gravitational force

the fundamental forces are those forces that act between to objects or element to make interactions. there are four types of fundamental forces such as strong and weak nuclear forces (due to protons and electrons), electromagnetic force (due to the motion of electrons) and gravitational force (due to orbital movement of the planet). if these forces are arranged on the basis of their maximum strength then the order is

strong nuclear force → electromegnetic force → weak nuclear force → gravitational force