Question

multiple choice
identify the choice that best completes the statement or answers the question.

1. determine the measure of ∠d to the nearest tenth of a degree.
2. determine the angle of inclination of the line to the nearest tenth of a degree.
3. determine the measure of ∠dbc to the nearest tenth of a degree.

Explanation:

Step1: Recall tangent - ratio formula

In a right - triangle, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$.

Step2: Solve for question 1

In right - triangle $DEF$, $\tan D=\frac{EF}{DE}$. Given $EF = 5$ and $DE=11$. Then $\tan D=\frac{5}{11}\approx0.4545$. So, $D=\arctan(0.4545)\approx24.4^{\circ}$.

Step3: Solve for question 2

For the angle of inclination of the line, if the vertical distance is $y = 4.4$ and the horizontal distance is $x = 9.9$, then $\tan\theta=\frac{4.4}{9.9}=\frac{4}{9}\approx0.4444$. So, $\theta=\arctan(0.4444)\approx24.0^{\circ}$.

Step4: Solve for question 3

In right - triangle $ABC$, $\tan\angle DBC=\frac{DC}{DB}$. First, find $\tan\angle ABC=\frac{AC}{AB}$. In right - triangle $ABC$ with $AB = 13$ and $BC = 6$, $\tan\angle ABC=\frac{6}{13}\approx0.4615$. $\angle DBC$ and $\angle ABC$ are the same in this context. $\angle DBC=\arctan(\frac{6}{13})\approx24.8^{\circ}$.

Answer:

1. B. $24.4^{\circ}$
2. C. $24.0^{\circ}$
3. B. $24.8^{\circ}$