The hiking path to the top of a mountain makes, at the steepest place, an angle of 20° with the horizontal, and it maintains this constant slope for 500 meters, as illustrated below. Which of the
following is the closest approximation to the change in elevation, in meters, over this 500-meter
section?
500 meters
20
A 20
B) 170
180
D 250

We are given:

a right angled triangle with the angle of elevation = 20 degrees

Hypotenuse of the Triangle = 500 m

Finding the change in Elevation:

We will use trigonometry in the given triangle to find the length of the perpendicular of the triangle

Using trigonometry, we found that the perpendicular = 500 * Sin 20 degrees

Perpendicular = 500 * 0.342           [sin(20 degrees) = 0.342]

Perpendicular = 171 m

The closest value to 171m in the given options is 170m

Therefore, 170m (option B) is correct

the answer to the expression is 83

step-by-step explanation: