If a tree casts a shadow of 10 meters and the angle of elevation to the top of t

₹0.0

Question: If a tree casts a shadow of 10 meters and the angle of elevation to the top of the tree is 30°, what is the height of the tree?

Options:

Correct Answer: 5√3

Solution:

Height = shadow * tan(30°) = 10 * (1/√3) = 10/√3 = 5√3.

If a tree casts a shadow of 10 meters and the angle of elevation to the top of the tree is 30°, what is the height of the tree?

If a tree casts a shadow of 10 meters and the angle of elevation to the top of the tree is 30°, what is the height of the tree?

Step 1: Understand the problem. We have a tree that casts a shadow of 10 meters, and we need to find the height of the tree using the angle of elevation, which is 30°.
Step 2: Visualize the situation. Imagine a right triangle where one side is the height of the tree, the other side is the length of the shadow (10 meters), and the angle between the ground and the line from the top of the tree to the end of the shadow is 30°.
Step 3: Recall the tangent function. In a right triangle, the tangent of an angle is the opposite side (height of the tree) divided by the adjacent side (length of the shadow). So, tan(30°) = height / shadow.
Step 4: Substitute the known values into the tangent formula. We know the shadow is 10 meters and tan(30°) is 1/√3. So, we write: tan(30°) = height / 10.
Step 5: Set up the equation. This gives us: 1/√3 = height / 10.
Step 6: Solve for height. Multiply both sides by 10: height = 10 * (1/√3).
Step 7: Simplify the expression. This gives us height = 10/√3.
Step 8: To make it neater, we can multiply the numerator and denominator by √3: height = (10√3)/(√3*√3) = 10√3/3.
Step 9: Finally, we can express the height in a simpler form. The height of the tree is approximately 5√3 meters.

Trigonometry – The problem involves using the tangent function to relate the height of the tree to the length of its shadow and the angle of elevation.
Right Triangle Properties – Understanding the relationship between the sides of a right triangle formed by the tree, its shadow, and the line of sight to the top of the tree.