Angles of Elevation/Depression

K

kaitllyn

New member
Joined
Apr 3, 2020
Messages
3
An observer is 150 meters from a mountain and is starting at the top of the mountain which is 341 meters tall. If the observers eye is 1.5 meters above the ground, what is the angle of elevation from the observers eye to the top of the mountain? Round to the nearest tenth.
 
You're going to have to draw a picture.

Do you know that angle of elevation is ALWAYS measured from the horizontal?
 
So, you're not going to draw a picture?

Draw a mountain. Make it 341 m tall. Decide what "150 meters from" means.
Draw an observer. Make this individual 1.5 m tall.
 
An angle is between two lines. One line is ALWAYS horizontal when it comes to measuring the angle of elevation. In your case the other line is the line from the observer's eyes to the top of the mountain.
 
kaitllyn said:
What does ["angle of elevation is always measured from the horizontal"] mean?
Click to expand...
Hi Kaitllyn. It means the initial ray of the angle is always horizontal, as shown below. (The situation is the same for angles of depression.)

In each case, the initial ray is shown as a horizontal, dotted line (the terminal ray is shown as a solid line).

AoE.JPG

?
 
Last edited:
Now please draw some other side(s) and label what you know. Please assume that the airplane is the top of the mountain.
 
I am not clear what "An observer is 150 meters from a mountain and is starting at the top of the mountain" means.

Is he on the mountain or is he 150 meters from it?
 
tkhunny said:
… Decide what "150 meters from" means …
Click to expand...
Yes, that piece of information could be better worded. My guess at the intent is for students to assume the observer is standing 150 meters from the "center" of the mountain's footprint (i.e., 150 meters from the point where a vertical line through the top of the mountain meets the ground). Otherwise, the exercise would need to provide additional information (like the incline of the mountain's slope, for example). The following restatement would not change those calculations.

An observer is 150 meters from the base of a vertical cliff, and they are staring at the top of the cliff which is 341 meters above the ground. If the observer's eye is 1.5 meters above the ground, what is the angle of elevation from the observers eye to the top of the cliff? Round to the nearest tenth of a meter.

I worked it both ways. If a student were to interpret the original wording to mean 150 meters from the closest point at the base of the mountain, instead of inside the mountain, and they arbitrarily chose a common mountain slope (40°), then their answer would be 34.7° smaller than what I think the author expects.

?
 
You must log in or register to reply here.
Top