Question

Use the law of cosines to find the value of cos theta. round your answer to two decimal places.

The opposite side of the theta is 5.7. Adjacent to the theta is 9.8.
Hypotenuse is 10.2

A. 0.35
B. 0.23
C. 0.84
D. 1.23

Answer 1

Use the law of cosines to find the value of cos theta. round your answer to two decimal places.
The opposite side of the theta is 5.7. Adjacent to the theta is 9.8.
Hypotenuse is 10.2

A. 0.35
B. 0.23
☆☆☆☆☆☆☆☆☆☆☆☆☆☆C. 0.84
D. 1.23

Answer 2

Answer: C) 0.84

Explanation:

Since According to the law of cosines ,

`b^2= a^2+b^2-2abcos\theta`

Where,

b is the opposite side of
`\theta`

And, a and b are the adjacent sides of
`\theta`.

Here, c= 5.7 , a = 9.8 and b= 10.2

Therefore,
`(5.7)^2 = (9.8)^2+(10.2)^2-2* 9.8* 10.2* cos\theta`

⇒
`32.49= 96.04+104.04 - 199.92* cos\theta`

⇒
`199.92* cos\theta= 200.08-32.49`

⇒
`cos\theta=167.49/199.92=0.83828531412`≈0.84

Thus, Option C is correct.