Question

Triangle A B C is shown. Angle A C B is a right angle. The length of hypotenuse A B is 13, the length of C B is 12, and the length of A C is 5. Angle C A B is x.

Which equation can be used to find the measure of angle BAC?

tan−1(StartFraction 5 Over 12 EndFraction) = x
tan−1(StartFraction 12 Over 5 EndFraction) = x
cos−1(StartFraction 12 Over 13 EndFraction) = x
cos−1(StartFraction 13 Over 12 EndFraction) = x

Answer 1

tan−1(StartFraction 12 Over 5 EndFraction) = x

Explanation:

Remember that tan is opposite/adjacent. The side opposite angle A is 12 and the side adjacent to angle A is 5. To find the angle, you must use the inverse of tangent.

Answer 2

`tan^(-1)((12)/(5) )=x`

Explanation:

The image attached shows the right triangle.

Now, in the image, observe that we already know all sides of the triangle, which means we can use any trigonometric reason.

If we use tangent, it would be

`tanx=(12)/(5)`

If we use cosine

`cosx=(5)/(13)`

If we use sin

`sinx=(12)/(13)`

Any equation of these can be used to find the angle.

Now, if you observe the given choices, notice that the only one which is correct is the second one

`tan^(-1)((12)/(5) )=x`

Therefore, the right answer is the second option.