Question

the angle of depression is measured from the top of a 43 ft tower to a reference point on the ground. its value is found to be 63°. how far is the base of the tower from the point on the ground?

Answer 1

An angle of depression is the angle of a slant to the upper horizontal line. The official definition is: the angle formed by the line of sight and the horizontal plane for an object below the horizontal.

Thus, for this problem, we must use trigonometry. The tower is perpendicular to the upper horizontal and the ground, so after we draw a line connecting the points we get 90 - 63 = 27, which is one of the angles in the right triangle.

The other angles are ninety and 63. We wish to find the measure of the bottom of the triangle, so we use tangent which includes both legs.

Therefore, tan(27)=x/43. Plugging this into a calculator, we get roughly 21.9.

Hope this helped! It probably sounds a lot harder than it actually is without a picture.