From the top of a tree, a bird looks down on a field mouse at an angle of depression of 50°. If the field mouse is 40 meters from the base of the tree, find the vertical distance from the ground to the bird's eyes. Round the answer to the nearest tenth.

Question

Mathematics

Reuben

29 October, 20:29

From the top of a tree, a bird looks down on a field mouse at an angle of depression of 50°. If the field mouse is 40 meters from the base of the tree, find the vertical distance from the ground to the bird's eyes. Round the answer to the nearest tenth.

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Nicholas Bright · Answer 1

We are given with an angle of depression of the bird to the field mouse of 50 degrees while the distance from the base tree to the mouse of 40 meters. To get the height of the bird from the ground, we take the tan of 50. We express tan 50 = height / base distance. tan 50 = height / 40 meters. Hence the height is 47.7 meters.