The height of the mountain estimated by two students is 2,467.98 meters.
<h3>
Height of the mountain </h3>
The height of the mountain is calculated as follows;
tanα = h/( a + b + x)
where;
- x is the distance between end of b and h
tan37 = h/(1850 + 740 + x)
tan37 = h/(2590 + x)
h = tan37(2590 + x)
h =1,951.82 + 0.7536x ---- (1)
tanβ = h/(b + x)
tan60 = h/(740 + x)
h = tan60(740 + x)
h = 1,281.68 + 1.732x ---- (2)
Solve (1) and (2) together
1,951.82 + 0.7536x = 1,281.68 + 1.732x
1,951.82 - 1,281.68 = 1.732x - 0.7536x
670.14 = 0.9784x
x = 684.93 m
h = 1,281.68 + 1.732x
h = 1,281.68 + 1.732(684.93)
h = 2,467.98 m
Thus, the height of the mountain estimated by two students is 2,467.98 meters.
Learn more about angle of elevation here: brainly.com/question/88158
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