To estimate the height of a mountain, two students find the angle of elevation from a point (at ground level) $b = 640$ meters from the base of the mountain to the top of the mountain is $β = 5 6^{\circ}$ . The students then walk $a = 2700$ meters straight back and measure the angle of elevation to now be $α = 3 8^{\circ}$ . 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.

Question

To estimate the height of a mountain, two students find the angle of elevation from a point (at ground level)

b = 640

meters from the base of the mountain to the top of the mountain is

β = 5 6^{\circ}

. The students then walk

a = 2700

meters straight back and measure the angle of elevation to now be

α = 3 8^{\circ}

. 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.

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