A person looks at the top of a tree from a distance of 40 meters. If the angle o

A person looks at the top of a tree from a distance of 40 meters. If the angle of elevation is 30 degrees, what is the height of the tree?

A person looks at the top of a tree from a distance of 40 meters. If the angle of elevation is 30 degrees, what is the height of the tree?

Correct Answer: 20 meters

Step 1: Understand the problem. You need to find the height of a tree when you know the distance from the tree and the angle you are looking up at the top of the tree.
Step 2: Identify the distance from the person to the tree. In this case, it is 40 meters.
Step 3: Identify the angle of elevation. Here, it is 30 degrees.
Step 4: Use the tangent function. The formula to find the height (h) of the tree is: h = distance * tan(angle).
Step 5: Substitute the values into the formula. So, h = 40 * tan(30 degrees).
Step 6: Calculate tan(30 degrees). The value of tan(30 degrees) is 1/√3 (approximately 0.577).
Step 7: Multiply the distance by the tangent value. So, h = 40 * (1/√3).
Step 8: Calculate the height. This gives you approximately 20 meters.

Trigonometry – The problem involves using the tangent function to relate the angle of elevation to the height of the tree and the distance from the observer.
Right Triangle Properties – Understanding the relationship between the sides of a right triangle formed by the height of the tree, the distance from the observer, and the angle of elevation.