An advertising blimps hovers over stadium at the altitude of 152 m.the pilot sites a tennis court at in 80 degree angle of depression. Find the ground distance in the straight line between the stadium and the tennis court. (note: in an exercise like this one, and answers saying about .....hundred meters is sensible.)
889.4
To find the ground distance in a straight line between the stadium and the tennis court, we can use trigonometry.
Let's denote the ground distance as d. We know that the height of the blimp (152 m) forms a right angle with the ground distance (d) and an angle of depression (80 degrees) with the line of sight to the tennis court.
Using trigonometry, we can use the tangent function to relate the angle of depression to the sides of the right triangle formed by the height of the blimp and the ground distance. The tangent function is defined as the ratio of the opposite side to the adjacent side:
tan(angle of depression) = opposite/adjacent
In this case, the opposite side is the height of the blimp (152 m) and the adjacent side is the ground distance (d):
tan(80 degrees) = 152/d
Now, we can solve for d. Rearranging the equation:
d = 152 / tan(80 degrees)
Using a scientific calculator or an online calculator, evaluating the tangent of 80 degrees:
d ≈ 152 / 5.6713
d ≈ 26.81 meters
So, the ground distance in a straight line between the stadium and the tennis court is approximately 26.81 meters.