Question

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

Answer 1

Answer:

m=$7\sqrt3$

n=7

Step-by-step 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 $\frac{a}{2}$, and the leg opposite from the 60 degree angle is $\frac{a\sqrt3}{2}$

In this case, a=14, n=$\frac{a}{2}$, and m=$\frac{a\sqrt3}{2}$

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=$\frac{14}{2}$, which is equal to 7

And m=$\frac{14\sqrt3}{2}$, which simplified, is equal to $7\sqrt3$

Hope this helps!