Question

The shadow of a tree is 10m longer when the angle of elevation of the sun is 450 than when it is 60 Find the height of the tree leaving your answer in surd form​

Answer 1

To find the height of a tree based on its shadow lengths at different angles of elevation, we use trigonometry. The height expressed in surd form is 10 / (1 - 1/√3) meters.

Step-by-step explanation:

The question involves finding the height of a tree (h) given the lengths of its shadows when the angle of elevation of the sun is 45° and 60°, respectively. We can use trigonometry to solve this problem.

Let the length of the shadow when the angle is 45° be s meters. Therefore, when the angle is 60°, the shadow's length will be s - 10 meters, as the shadow is 10m longer at 45°.

Using the tangent function for angle of 45°:

• tan(45°) = h/s
• 1 = h/s (since tan(45°) = 1)
• h = s ... (1)

Using the tangent function for angle of 60°:

• tan(60°) = √3 = h/(s - 10)
• s - 10 = h/√3 ... (2)

Substitute equation (1) into equation (2):

• s - 10 = s/√3
• s(1 - 1/√3) = 10
• s = 10 / (1 - 1/√3)

Now, substitute s back into equation (1) to find the height of the tree:

• h = 10 / (1 - 1/√3)

Therefore, the height of the tree, expressed in surds, is 10 / (1 - 1/√3) meters.