a) We can use trigonometry to find the distance of the base of the ladder from the tree. Let x be the distance we want to find.
cos(70°) = x/7
x = 7cos(70°)
x ≈ 2.30 m
Therefore, the base of the ladder is approximately 2.30 m from the tree.
b) The angle of depression is the angle between Kevin's line of sight and the horizontal. Since we know the distance to the basket and the height of the ladder, we can use trigonometry to find this angle. Let θ be the angle of depression.
tan(θ) = (height of ladder) / (distance to basket + distance from ladder base to tree)
tan(θ) = 7 / (5.4 + 2.30)
tan(θ) ≈ 0.849
θ ≈ 40°
Therefore, the angle of depression is approximately 40°.
Kevin is standing at the top of a ladder. The ladder is 7 m long. It is propped against a tree, and makes an
angle of 70° with the ground. To check his aim, Kevin is tossing balls into a basket located 5.4 m from the
base of the ladder, on the opposite side of the tree.
a) Determine the distance of the base of the ladder from the tree, in metres.
b) If Kevin’s eyes are even with the top of the ladder and he looks down on the basket, what is the angle of
depression? Answer to the nearest degree.
1 answer
1 answer