Question

1. determine the measures of ∠a and ∠c to the nearest tenth of a degree.

Explanation:

Step1: Find $\tan C$

In right - triangle $BCD$, $\tan C=\frac{BD}{CD}=\frac{4}{3}$.

Step2: Calculate $\angle C$

$\angle C=\arctan(\frac{4}{3})\approx53.1^{\circ}$ (using a calculator, $\arctan(x)$ gives the angle whose tangent is $x$).

Step3: Find $\angle A$

Since $\angle B = 90^{\circ}$ in $\triangle ABC$, and the sum of angles in a triangle is $180^{\circ}$, $\angle A+\angle B+\angle C = 180^{\circ}$. So $\angle A=180^{\circ}-90^{\circ}-\angle C$. Substituting $\angle C\approx53.1^{\circ}$, we get $\angle A = 36.9^{\circ}$.

Answer:

$\angle A\approx36.9^{\circ}$, $\angle C\approx53.1^{\circ}$