Here angle of elevation is 60And base is shadow of 14mLet the height of tree be 'X'Now using,Tan 60 = x/14root 3 = x/14 x = 14 * root over 3Therefore the height of tree is 14rootover3 metres

Problem: Find the height of a tree which casts a shadow 14m long on the ground when the angle of elevation of the sun is 60°.

Solution:

To find the height of the tree, we can use the trigonometric relationship between the angle of elevation, the height of the tree, and the length of its shadow. Let's break down the problem step-by-step.

Step 1: Understanding the problem.
We are given the length of the shadow on the ground, which is 14m, and the angle of elevation of the sun, which is 60°. We need to find the height of the tree.

Step 2: Drawing a diagram.
To visualize the problem, let's draw a diagram. Draw a vertical line to represent the tree, and a horizontal line to represent the ground with the shadow. Mark the angle of elevation of 60° between the ground and the line representing the height of the tree.

Step 3: Identifying the trigonometric relationship.
We can use the tangent function to relate the angle of elevation, the height of the tree, and the length of the shadow. The tangent of an angle is equal to the ratio of the opposite side to the adjacent side in a right triangle.

Step 4: Applying the tangent function.
Let's use the tangent function to write the equation for our problem:

tan(60°) = height of the tree / length of the shadow

Step 5: Solving the equation.
We can now solve the equation for the height of the tree:

tan(60°) = height of the tree / 14m

To isolate the height of the tree, we can multiply both sides of the equation by 14m:

14m * tan(60°) = height of the tree

Using a calculator, we can determine the value of tan(60°) to be √3.

So, the height of the tree is:

14m * √3 ≈ 24.25m

Therefore, the height of the tree is approximately 24.25m.