Question

a road is inclined at an angle of 3°. after driving 5,356 feet along this road, find the drivers increase in altitude. round to the nearest foot. the drivers increase in altitude is \\(\square\\) ft. (simplify your answer.)

Explanation:

Step1: Identify trigonometric ratio

We use the sine function, since $\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$, where the opposite side is the altitude $a$, hypotenuse is 5356 ft, and $\theta=3^\circ$.

Step2: Rearrange to solve for $a$

Rearrange the formula to isolate $a$: $a = 5356 \times \sin(3^\circ)$

Step3: Calculate the value

First, ensure calculator is in degree mode. $\sin(3^\circ) \approx 0.05234$
$a \approx 5356 \times 0.05234$
$a \approx 280.3$

Step4: Round to nearest foot

Round 280.3 to the nearest whole number.

Answer:

280