Question

In ΔQRS, the measure of ∠S=90°, RQ = 41, QS = 9, and SR = 40. What is the value of the cosine of ∠R to the nearest hundredth?

Answer 1

Answer:

cos R = .98

Step-by-step explanation:

cos R = SR/QR

QR is the hypotenuse of the right triangle.  By the Pythagorean theorem

(QR)^2 = (QS)^2 + (SR)^2

           = 9^2 + 40^2

           = 81 + 1600

           = 1681

QR = 41

Cos R = adjacent side/hypotenuse = 40/41 = .98

 

Answer 2

The value of the cosine of ∠R to the nearest hundreth is  0.98.

What is a right angle triangle?

A right angle triangle has one of its angles as 90 degrees. The sides and angles can be found using trigonometric ratios.

The sides can also be found using pythagoras theorem. Therefore,

∠S = 90°

RQ = 41

QS = 9

SR = 40

cos R = adjacent / hypotenuse

Therefore,

adjacent side = 40

hypotenuse = 41

cos R = 40 / 41

cos R = 0.97560975609

cos R = 0.98

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