Question

What is measure of angle R?

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

°
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

Answer:

The measure of angle R is $22.62\°$

Step-by-step explanation:

we know that

In the right triangle PQR

The cosine of angle R is equal to divide the adjacent side angle R by the hypotenuse

so

$cos(R)=\frac{QR}{PR}$

substitute the values

$cos(R)=\frac{12}{13}$

$<R=arccos(\frac{12}{13})=22.62\°$

see the attached figure to better understand the problem

Answer 2

Answer:

$R=22.64^{\circ}$

Step-by-step explanation:

Given: PQR is a right angled triangle which is right angled at Q and PQ=5cm, QR=12cm and PR=13cm.

To find: The measure of the angle R.

Solution: It is given that PQR is a right angled triangle which is right angled at Q and PQ=5cm, QR=12cm and PR=13cm.

Using trigonometry, we have

$\frac{PQ}{QR}=tanR$

Substituting the given values, we have

⇒$\frac{5}{12}=tanR$

⇒$0.417=tanR$

⇒$R=tan^{-1}(0.417)$

⇒$R=22.64^{\circ}$

thus, the measure of angle R is 22.64°.