Question

A road is inclined at an angle of 5º. Afterdriving 4,955 feet along this road, find thedriver's increase in altitude. Round to thenearest foot.

Answer 1

Given:

Angle of inclination = 5 degrees

Distance = 4,955 feet

Let's find the driver's altitude.

Let's first sketch a figure which represents this situation.

To find the altitude, apply the trigonometric ratio for sin:

`\sin \theta=\frac{\text{opposite}}{\text{hypotenuse}}`

Where:

The opposite side is the altitude

The hypotenuse = 4955 ft.

θ = 5 degrees

Thus, we have:

`\sin 5=\frac{\text{altitude}}{4955}`

Multiply both sides by 4955:

`\begin{gathered} 4955\sin 5=\frac{\text{altitude}}{4955}*4955 \\ \\ 431.9=altitude \\ \\ \text{altitude= 431.9 ft}\approx432\text{ ft} \end{gathered}`

Therefore, the dirver's increase in altitude is 432 ft.

ANSWER:

432 feet