elevation and speed problem

[dewykitten13]

A motorist traveling along a level highway at a speed of 65 mph directly toward a mountain, observes that after traveling for 15 minutes the angle of elevation has changed from 10 to 55 degrees. What is the height of the mountain in feet?

I am having problems setting this up. Could someone please help me.

 

[wjm11]

A motorist traveling along a level highway at a speed of 65 mph directly toward a mountain, observes that after traveling for 15 minutes the angle of elevation has changed from 10 to 55 degrees. What is the height of the mountain in feet?

Draw a picture of the mountain and where the car is at two different times (15 minutes apart).

Connect the top of the mountain and the two car positions with lines. You now have a triangle. Write down the angles that you know on the picture as well.

Calculate how far the car traveled in 15 minutes. That is one side of the triangle.

Since you have one side of the triangle and you know the angles in the triangle, you can solve the other sides of the triangle (using Law of Sines or Law of Cosines). Either triangle side can be used to help find the height of the mountain.

Now draw a line straight down from the top of the mountain, intersecting the horizontal line that represents ground level. Along with the line to one of the car positions, you now have a right triangle formed. Solve for the height of the mountain.

 

[dewykitten13]

I am still having problems visualizing this. I got that the car traveled 16 miles in 15 minutes. The angle from the first point of the car is 10 degrees and the angle from the second car point is 55 degree. I just can't fit this all together.

 

[wjm11]

I am still having problems visualizing this. I got that the car traveled 16 miles in 15 minutes. The angle from the first point of the car is 10 degrees and the angle from the second car point is 55 degree. I just can't fit this all together.

Did you draw a picture?

The 55 degree angle is outside the triangle you drew, but it reveals one of the angles inside the triangle. (Hint: 180 - 55)

Also, I recommend that you do not round off your calculations until you reach your final answer. The distance traveled is 16.25 miles.