Final answer:
The angle of depression from the top of the lighthouse to Thomas can be found using the tangent function, with the height of the lighthouse as the opposite side and the distance from the lighthouse as the adjacent side. Taking the inverse tangent of this ratio gives the angle of elevation, which is equal to the angle of depression from the top of the lighthouse.
Step-by-step explanation:
The question involves finding the angle of depression from the top of a lighthouse to a person standing on the ground away from it. The height of the lighthouse is given as 75 yards and the horizontal distance from the person to the base of the lighthouse is 65 yards. To find the angle of depression, we can use trigonometric ratios, specifically, the tangent function, which relates the opposite side (height of the lighthouse) to the adjacent side (distance from the person to the base of the lighthouse).
We use the formula: tangent of the angle = opposite/adjacent
tan(angle) = 75/65
To find the angle, we take the inverse tangent (tan-1) of 75/65:
angle = tan-1(75/65) = tan-1(1.1538...)
The calculated angle is the angle of elevation from the ground to the top of the lighthouse. Since the angle of depression from the top of the lighthouse is equal to the angle of elevation from the ground (due to alternate interior angles in parallel lines), the required angle of depression is the same as the calculated angle.