A tree casts a shadow of 20 m when the angle of elevation of the sun is 30 degre

A tree casts a shadow of 20 m when the angle of elevation of the sun is 30 degrees. What is the height of the tree?

A tree casts a shadow of 20 m when the angle of elevation of the sun is 30 degrees. What is the height of the tree?

Correct Answer: 11.55 m

Step 1: Understand that the angle of elevation is the angle between the ground and the line from the top of the tree to the sun.
Step 2: Recognize that the shadow of the tree and the height of the tree form a right triangle with the ground.
Step 3: Identify the angle of elevation of the sun, which is given as 30 degrees.
Step 4: Use the tangent function, which relates the angle to the opposite side (height of the tree) and the adjacent side (length of the shadow).
Step 5: Write the equation: tan(30°) = height / shadow length. Here, shadow length is 20 m.
Step 6: Substitute the values into the equation: tan(30°) = height / 20.
Step 7: Recall that tan(30°) is equal to 1/√3.
Step 8: Set up the equation: 1/√3 = height / 20.
Step 9: Solve for height by multiplying both sides by 20: height = 20 / √3.
Step 10: Calculate the height: height ≈ 20 / 1.732 ≈ 11.55 m.

Trigonometry – The problem involves using the tangent function to relate the height of the tree to the length of its shadow based on the angle of elevation of the sun.
Angle of Elevation – Understanding how the angle of elevation affects the relationship between the height of an object and the length of its shadow.