Question

Find the missing side lengths leave your answer as a racials simplest form

Answer 1

m=
`7\sqrt3`

n=7

Explanation:

Hi there!

We are given a right triangle (notice the 90°) angle, the measure of one of the acute angles as 60°, and the measure of the hypotenuse (the side OPPOSITE from the 90 degree angle) as 14

We need to find the lengths of m and n

Firstly, let's find the measure of the other acute angle

The acute angles in a right triangle are complementary, meaning they add up to 90 degrees

Let's make the measure of the unknown acute angle x

So x+60°=90°

Subtract 60 from both sides

x=30°

So the measure of the other acute angle is 30 degrees

This makes the right triangle a special kind of right triangle, a 30°-60°-90° triangle

In a 30°-60°-90° triangle, if the length of the hypotenuse is a, then the length of the leg (the side that makes up the right angle) opposite from the 30 degree angle is
`(a)/(2)`, and the leg opposite from the 60 degree angle is
`(a\sqrt3)/(2)`

In this case, a=14, n=
`(a)/(2)`, and m=
`(a\sqrt3)/(2)`

Now substitute the value of a into the formulas to find n and m to find the lengths of those sides

So that means that n=
`(14)/(2)`, which is equal to 7

And m=
`(14\sqrt3)/(2)`, which simplified, is equal to
`7\sqrt3`

Hope this helps!