Calculate the height of a mountain from a oint A on a level plain, the angle of elevation of the top of the mountain was found to be 32°. At point B nearer the mountain, where |AB|=400m, the angle of elevation was found to be 58°
Let the height of the mountain be h and the distance from point A to the base of the mountain be d.
Using trigonometry, we can set up the following equations:
1) tan(32°) = h/d
2) tan(58°) = h/(d-400)
Solving for h in the first equation, we get:
h = d*tan(32°)
Substitute h in the second equation and solve for d:
tan(58°) = d*tan(32°)/(d-400)
tan(58°)(d-400) = d*tan(32°)
d*tan(58°) - 400*tan(58°) = d*tan(32°)
d(tan(58°) - tan(32°)) = 400*tan(58°)
d = 400*tan(58°)/(tan(58°) - tan(32°))
d ≈ 400 * 1.672 / (1.376 - 0.624)
d ≈ 400 * 1.672 / 0.752
d ≈ 887.09 meters
Now, substitute d back into the first equation to find h:
h = 887.09 * tan(32°)
h ≈ 887.09 * 0.624
h ≈ 553.65 meters
Therefore, the height of the mountain is approximately 553.65 meters.