Question

a road is inclined at an angle of ( 5^{circ} ). after driving 5100 feet along this road, find the drivers increase in altitude. round to the nearest foot. the drivers increase in altitude is about ( square ) feet. (round to the nearest whole number as needed.)

Explanation:

Step1: Use the sine function

In a right - triangle \(ABC\) (where \(AB = 5100\) is the hypotenuse, \(BC=a\) is the side opposite the angle \(\theta = 5^{\circ}\)), the sine function is defined as \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). So, \(\sin(5^{\circ})=\frac{a}{5100}\).

Step2: Solve for \(a\)

We can rewrite the equation from Step 1 as \(a = 5100\times\sin(5^{\circ})\).
We know that \(\sin(5^{\circ})\approx0.08716\). Then \(a = 5100\times0.08716\).

$$a=5100\times0.08716 = 444.516$$

Answer:

\(445\)