Can you help with this question (math whizzes)...?

Question

At a point A on the ground the angle of elevation of a mountain due east is 16.6°, and at B, due south of the mountain, the angle of elevation is 12.3°. If the mountain is 960metres high, find the distance from A to B, correct to one decimal place

(Note: I think I have to draw this, I can't visualise on a flat diagram/scale diagram where point B would be-Is it a 3-D shape?). Could you please help me and explain to me what the diagram. Thankyou.

PS: Could you please email me what the diagram (where the points should go). I can't work it out. Do I put a dot in the middle for the base of the mountain, a dot to the left of it at the horizontal called A, a dot a few cm's underneath the base of the mountain called B and a dot directly above the base of the mountain which is the top of the mountain? Where is the 12.3 degrees? Please help. Thankyou.

Answer 1

Use three separate triangles for this.

First, calculate the distance from A to the base of the mountain (call this P). Use a triangle with a right angle at P, a 16.6° angle at A and a height of 960m opposite A. You need to find the length of the side joining A to the right angle (i.e. not the hypotenuse). You should get AP = 960 / tan 16.6° = 3220.26 m (2 d.p.)

Now, do the same thing with a similar sort of triangle for B to get the distance BP.

Now, use a third right-angled triangle containing A, B and P. We know P is due east of A and due north of B, so angle APB is a right angle. You know AP and BP, so Pythagoras' theorem will get you AB.