Question

What’s the answer pls

Answer 1

Option B
`(24)/(7)`

Explanation:

Tangent is opposite / adjacent. Since T is the vertex at which the ratio needs to be determined, start from T.

The opposite side of vertex T is 48. It cannot be 50, since it is the hypotenuse (opposite cannot be the hypotenuse). So, the first part of the ratio will be 48.

At this point, the ratio looks like this:
`(48)/(b)`.

The adjacent side is segment ST. This number is unknown. In order to find it, use Pythagorean Theorem. We know the hypotenuse and one of the legs, so plug the numbers in and use algebra to solve.

`a^2+b^2=c^2`

`48^2+b^2=50^2`

`2304+b^2=2500`

`b^2=196`

`b=√(196)`

`b=14`

Now that the length of the segment ST has been identified, we can place the adjacent side, 14, as the denominator of the ratio.

This means that the ratio looks like this:
`(48)/(14)`. However, it can be simplified. Divide the numerator and denominator by their GCF, 2.

48 divided by 2 is 24.

14 divided by 2 is 7.

So, the ratio now looks like this
`(24)/(7)`.

That means the answer is (b).