Question

Can someone help me with this please asap? thank you so much

Answer 1

`\\\cos B =(8√(79))/(79)`

Explanation:

How do we find cosine of an angle in a right triangle?
In a right-angled triangle, if one of the angles is θ, then the cosine of θ is the length of the side adjacent to θ, divided by the length of the hypotenuse .

Here we are trying to find cos B

The side adjacent to B is BC with a length of
`8`

The hypotenuse is BD with a length of
`√(79)`

`\therefore\\\cos B = (8)/(√(79))\\`

`79` is a prime number so it cannot be factored

To express in simplest radical form, we have to remove
`√(79)` from the denominator by multiplying the numerator and denominator by
`√(79)`

`\therefore\\\cos B = (8)/(√(79)) * (√(79))/(√(79)) \\\\= (8√(79))/(79)`