Question

In right triangle PQR , PQ=12 cm and QR=5cm .What is cos R?

Answer 1

Answer:

Cos R=0.384615384615

Step-by-step explanation:

We are given a right angled triangle PQR

PQ = 12 cm

QR = 5cm

PR = hypotenuse

Refer the attached figure .

To Find length of hypotenuse , we will use Pythagoras Theorem .

$Hypotenuse ^2 = Perpendicular ^2 +Base^2$

$PR ^2 = PQ ^2 +QR^2$

$PR ^2 =12 ^2 +5^2$

$PR ^2 =144 +25$

$PR ^2 =169$

$PR =13$

Now to find Cos R we will use trigonometric ratio :

$Cos\theta = \frac{Base}{Hypotenuse}$  

$Cos R = \frac{QR}{PR}$  

$Cos R= \frac{5}{13}$  

$Cos R=0.384615384615$  

$R=Cos^{-1} 0.384615384615$  

$R=67.3^{\circ}$  

Answer 2

Concept

Trigonometric ratios are the ratios of the sides of the right angled ratios.

Given

In a triangle PQR, PQ=12 cm and QR=5 cm.

To find

cos R?

Explanation

In the right angled triangle angle PQR is 90°. So the hypotenuse will be calculated as:

PR=$\sqrt{PQ^{2} +QR^{2} }$

PR=$\sqrt{12^{2}+5^{2} }$

PR=$\sqrt{144+25}$

PR=$\sqrt{169}$

PR=13 cm

Cos theta=B/H

Cos R= 5/13

Hence the value of cos R is 5/13.

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