in right triangle PQR,Q=90DEGREE,PQ=4 AND PR=7 WHAT IS ANGLE R TO THE NEARST TENTH OF A DEGREE

(PQ)^2 + (QR)^2 = (PR)^2,

4^2 + (QR)^2 = 7^2,
(QR)^2 = 7^2 - 4^2 = 49 - 16 = 33,
QR = 5.7.

cosR = QR/PR = 5.7/7 = 0.8207.
R = 34.8 deg.

To find angle R in a right triangle PQR, where Q is a right angle and PQ = 4, and PR = 7, you can use trigonometry.

First, recall the trigonometric function called tangent (tan). In a right triangle, tan(angle) is defined as the ratio of the length of the opposite side to the length of the adjacent side.

In this case, angle R is the opposite angle to side PR, and PQ is the adjacent side. So, we can calculate the tangent of angle R:

tan(R) = opposite / adjacent
tan(R) = PR / PQ
tan(R) = 7 / 4

Now, to find angle R, we can take the inverse tangent (arctan) of the tangent ratio we just calculated:

R = arctan(tan(R))

Substituting the value of the tangent ratio, we have:

R = arctan(7/4)

Using a calculator or a math software, you can determine the value of arctan(7/4). The final answer is angle R to the nearest tenth of a degree.