Question

What is the measure of angle P?

Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth.

​m∠P=​
°
P Q R is a right triangle. Q is a right angle. P Q is equal to five centimeters, Q R is equal to twelve centimeters and P R is equal to thirteen centimeters.

Answer 1

m∠P= 67.38

Explanation:

took the quiz and got it correct -k12

Answer 2

`\angle P\approx67.38\textdegree`

Explanation:

We want to find the measure of ∠P.

To do so, we can use one of the three trigonometric functions.

Since we know the lengths of all of the sides, it doesn't matter which one we use: we will get the same result.

Let's use the sine ratio. Recall that sine is the ratio of the opposite side to the hypotenuse. That is:

`\displaystyle \sin(x)=\frac{\text{opposite}}{\text{hypotenuse}}`

Substitute ∠P for x. So:

`\displaystyle \sin(\angle P)=\frac{\text{opposite}}{\text{hypotenuse}}`

The opposite side to ∠P is 12. The hypotenuse is 13. Hence:

`\displaystyle \sin(\angle P)=(12)/(13)`

We can take the inverse sine of both sides:

`\displaystyle \angle P=\sin^(-1)\left((12)/(13)\right)`

Use a calculator. Make sure you're in degrees mode!

So, the measure of our angle is:

`\angle P\approx67.38\textdegree`

And we're done!