We are given a fence of height 2.4 m and a tree of height 16 m. The fence is 10 m away from the tree. We want to find the angle of elevation of the top of the tree from the top of the fence.

1. Problem Description

We are given a fence of height 2.4 m and a tree of height 16 m. The fence is 10 m away from the tree. We want to find the angle of elevation of the top of the tree from the top of the fence.

2. Solution Steps

First, we need to find the difference in height between the top of the tree and the top of the fence.

Height difference = Tree height - Fence height

Height difference = $16 - 2.4 = 13.6$ m

Now, we can use the tangent function to find the angle of elevation. Let $\theta$ be the angle of elevation. Then,

$tan(\theta) = \frac{opposite}{adjacent} = \frac{height \ difference}{distance \ between \ fence \ and \ tree}$

$tan(\theta) = \frac{13.6}{10} = 1.36$

Now, we find the angle $\theta$ by taking the inverse tangent (arctan) of 1.

3

6. $\theta = arctan(1.36)$

$\theta \approx 53.67$ degrees.

3. Final Answer

The angle of elevation is approximately 53.67 degrees.

So the answer is B. 53.67°.