Question

clue # 7
a road is inclined at an angle of $6^\circ$. after driving 5,440 feet along this road, find the drivers increase in altitude. round to the nearest foot.
the drivers increase in altitude is ______ ft.
a 5,410
c 52,043
b 569
d 572

Explanation:

Step1: Identify trigonometric ratio

We use sine, since $\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}$, where the opposite side is the altitude increase $a$, hypotenuse is 5440 ft, and $\theta=6^\circ$.

Step2: Rearrange to solve for $a$

$a = 5440 \times \sin(6^\circ)$

Step3: Calculate the value

First, find $\sin(6^\circ)\approx0.104528$. Then $a\approx5440\times0.104528\approx568.63$

Step4: Round to nearest foot

$a\approx569$

Answer:

B 569