Question

Can someone PLEASE help me out??!!!!!!!

Answer 1

`\huge\boxed{66.42 \textdegree}`

Explanation:

In order to solve for this missing angle, we can use trigonometry.

With angle B, we only have two sides: the adjacent of the angle and the hypotenuse of the angle. The adjacent side is the one laying directly next to the angle that isn't the hypotenuse.

Using SOH CAH TOA, we can see that the correct trig function for this would be cos because of CAH (Cosine = Adjacent over Hypotenuse)

Since we know the length of the sides but we don't know the angle, we are going to use inverse trig.

The adjacent side over our hypotenuse will be
`(2)/(5)` since 2 is the length of the adjacent and 5 is the length of the hypotenuse.

We know have the equation
`cos^(-1)(B) = (2)/(5)`.

We now find what
`(2)/(5)` is (0.4) and find the inverse cosine of it. We can do this by plugging it into a calculator.

When we do this, we get the number
`66.42182152` etc. Rounding to the nearest hundredth gets us 66.42.

Hope this helped!