Question

Given the following triangle, if a = 12 and ∠B = 48°, find b to the nearest whole number.

Answer 1

The value of b nearest whole number is, 13.

Explanation:

We know an
`\angle B=48^(\circ)` and the side adjacent to it i.e, a=12.\

In a right triangle BCA ,

the tangent(tan) of an angle is the length of the opposite side divided by the length of the adjacent side.

i.e,
`\tan B=(opposite)/(Adjacent)=(b)/(a)`

Substitute the value of a=12 and
`\angle B=48^(\circ)` to solve for b in above expression:

`\tan 48^(\circ)=(b)/(12)`

we have the value of
`\tan 48^(\circ)=1.110613`

then,
`1.20012724=(b)/(12)`

On simplify we get,

`b=1.110613 * 12=13.327356`

Therefore, the value of b nearest whole is, 13

Answer 2

In the figure, the triangle ABC is a right triangle, a is the adjacent leg to the angle B, and b is the opposite side to the same angle.

So, you can use the tangent ratio which relates the angle, the opposite leg and the adjacent leg:

tangent (angle B) = b / a => b = a * tan(B)

=> b = 12 * tan(48°) = 13.33≈ 13

Answer: 13