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[Worth 30 Points] NEED HELP!!!

To estimate the height of a mountain, two students find the angle of elevation from a point (at ground level) b=740meters from the base of the mountain to the top of the mountain is β=60∘. The students then walk a=1850 meters straight back and measure the angle of elevation to now be α=37∘. If we assume that the ground is level, use this information to estimate the height of the mountain.

The height of the mountain is: ______ Meters.

Explain how your answer measure below. Be sure to show all of your work.

Worth 30 Points NEED HELP To Estimate The Height Of A Mountain Two Students Find The Angle Of Elevation From A Point At Ground Level B740meters From The Base Of class=

Sagot :

onyebuchinnaji

The height of the mountain estimated by two students is 2,467.98 meters.

Height of the mountain

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: https://brainly.com/question/88158

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