Question

description the midterm exam covers material from chapters 1 - 5. instructions from the list of choices, select the one best answer. multiple attempts not allowed. this test can only be taken once. force completion this test can be saved and resumed later. your answers are saved automatically. question completion status: question 2 1 points save answer a certain mountain road is inclined 3.1° with respect to the horizon. what is the change in altitude of the car as a result of its traveling 2.90 km along the road? 289 m 116 m 157 m 203 m 181 m

Explanation:

Step1: Convert distance unit

Convert \(2.90\) km to meters. Since \(1\) km \( = 1000\) m, then \(d=2.90\times1000 = 2900\) m.

Step2: Use sine function

We know that in a right - triangle (where the road is the hypotenuse, the change in altitude \(h\) is the opposite side with respect to the angle of inclination \(\theta = 3.1^{\circ}\)), the sine function is defined as \(\sin\theta=\frac{h}{d}\).
So, \(h = d\sin\theta\).
Substitute \(d = 2900\) m and \(\theta=3.1^{\circ}\) into the formula. We know that \(\sin(3.1^{\circ})\approx0.054\) (using a calculator, \(\sin x\) where \(x\) is in degrees).
Then \(h=2900\times0.054\)
\(h = 156.6\approx157\) m

Answer:

157 m