Question

1. in △abc, ab = 3 and ac = 9. find m∠b to the nearest degree.

72
52
58
18

Explanation:

Step1: Identify the triangle type

$\triangle ABC$ is a right triangle with $\angle A = 90^\circ$, $AB = 3$ (opposite to $\angle C$), and $AC = 9$ (opposite to $\angle B$).

Step2: Use trigonometric ratio

For $\angle B$, $\tan(B)=\frac{\text{opposite}}{\text{adjacent}}=\frac{AC}{AB}$. Substitute $AC = 9$ and $AB = 3$:
$\tan(B)=\frac{9}{3}=3$

Step3: Find the angle

To find $m\angle B$, take the arctangent:
$m\angle B=\arctan(3)$
Calculate $\arctan(3)\approx71.565^\circ$, which rounds to $72^\circ$.

Answer:

72