Question

If 8 cot theta=15,then cos theta is

Answer 1

The value of cos θ = 15/17

Given:

8 cot θ = 15

To find:

The value of cos θ

Solution:

Given that 8 cot θ = 15

⇒ cot θ = 15/ 8

As we know in a right angled triangle

cot θ = adjacent /opposite

From given data $\frac{adj side}{opp side} = \frac{15}{8}$  

⇒ adjacent side = 15

⇒ opposite side = 8

From Pythagorean theorem

⇒ Hypotenuse² = Adjacent² + opposite²  

⇒ Hypotenuse² = 15² + 8²  

⇒ Hypotenuse² =  289

⇒  Hypotenuse² =  17²

⇒  Hypotenuse = 17  

In a right angle triangle cos θ = Adjacent / hypotenuse

⇒ cos θ = 15/17

The value of cos θ = 15/17

#SPJ2

Answer 2

Answer:

The answer to the given question is

$\cos(theta) = \frac{15}{17}$

Step-by-step explanation:

Given :

8 cot theta = 15.

To find :

cos theta =?.

Solution :

It is given that 8 cot theta = 15.

Then

$\cot(theta) = \frac{15}{8}$

In a right-angled triangle, the value of the cot theta will be obtained as the division of the adjacent side by the opposite side.

From the given data it is observed that

$\cot(theta) = \frac{adjacent \: side}{opposite \: side} = \frac{15}{8}$

From this, the adjacent side is 15 and the opposite side is 8.

From the Pythagoras theorem,

the sum of the square of two sides is equal to the square of the hypotenuse.

${hypotenuse}^{2} = {adjacent}^{2} + {opposite}^{2}$

let the hypotenuse be x.

${x}^{2} = {15}^{2} + {8}^{2}$

On solving, we get the answers as

${x}^{2} = 225 + 64 \\ {x}^{2} = 289$

on cancelling the square, we get the value as

289.

$x = \sqrt{289} \\ x = 17$

The value of cos theta will be obtained as the division of adjacent by the hypotenuse

$\frac{adjacent}{hypotenuse} = \cos(theta)$

cos theta =

$\frac{15}{17}$

Therefore, the final answer to the given question is

$\frac{15}{17}$

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