Step-by-step explanation:

Let's analyze the problem using trigonometry. We have a tree that forms a 7-degree angle with the vertical, and a 24-degree angle formed by looking at the top of the tree from a point on the ground 40 feet away from its base.

First, let's consider the angle of the tree relative to the ground. The tree forms a 7-degree angle with the vertical. Since the vertical is perpendicular to the ground, their angle sum would be 90 degrees. Thus, the angle at the base of the tree (relative to the ground) will be:

90° - 7° = 83°

Now let's use this angle (83°) in the triangle formed by the base of the tree, the point on the ground 40 feet away from the base, and the top of the tree. We are given one side of this triangle (40 feet) and an angle (83°) directly opposite to the length we want to find. We can use the tangent ratio to determine the length of the tree:

Let "t" be the length of the tree, then:

tan(83°) = t / 40 ft

To find the tree length "t," multiply both sides by 40 ft:

t = 40 ft * tan(83°)

To solve for the length "t," use a calculator to compute the tangent of 83 degrees:

t = 40 ft * 9.5175 (approximated)

t ≈ 380.7 ft

Hence, the length of the tree is approximately 380.7 feet.