Question

$\angle b = \square ^\circ$
round your answer to the nearest hundredth.

Explanation:

Step1: Identify trigonometric ratio

We use sine: $\sin(\angle B) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{AC}{AB}$. First find $AC$ via Pythagoras:
$AC = \sqrt{AB^2 - BC^2} = \sqrt{7^2 - 2^2} = \sqrt{49-4} = \sqrt{45} = 3\sqrt{5}$

Step2: Calculate sine of $\angle B$

$\sin(\angle B) = \frac{3\sqrt{5}}{7} \approx \frac{6.7082}{7} \approx 0.9583$

Step3: Find $\angle B$ via arcsine

$\angle B = \arcsin(0.9583)$

Answer:

$73.61^\circ$