Question

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

Answer 1

Answer:

The value of b nearest whole number is, 13.

Step-by-step 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, $\tan B=\frac{opposite}{Adjacent}=\frac{b}{a}$

Substitute the value of a=12 and $\angle B=48^{\circ}$ to solve for b in above expression:

$\tan 48^{\circ}=\frac{b}{12}$

we have the value of $\tan 48^{\circ}=1.110613$

then, $1.20012724=\frac{b}{12}$

On simplify we get,

$b=1.110613 \times 12=13.327356$

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