Find the angle of depression of a boat from the bridge at a horizontal distance of 25 m from the bridge if the height of the bridge is 25 m
tan angle = 25/25
angle = 45 degrees
plz solf answer
tan 25 /25
angle 45 why
To find the angle of depression, we can use trigonometry.
The angle of depression is the angle formed between the line of sight from an observer (on the bridge) to a lower point (the boat) and the horizontal plane.
In this case, we have a right-angled triangle, with the height of the bridge as the vertical side (opposite side) and the horizontal distance from the bridge as the horizontal side (adjacent side). We are looking for the angle of depression, which is the angle between the horizontal side and the hypotenuse of the triangle.
Let's denote the angle of depression as θ.
Using trigonometry, we can use the tangent function to calculate θ:
tangent(θ) = opposite/adjacent
In this case, the opposite side is the height of the bridge (25 m) and the adjacent side is the horizontal distance from the bridge (25 m).
Therefore, tangent(θ) = 25/25 = 1
To find θ, we take the inverse tangent (or arctan) of both sides:
θ = arctan(1)
Using a calculator, we can find the inverse tangent of 1 to be approximately 45 degrees.
Therefore, the angle of depression of the boat from the bridge is approximately 45 degrees.