A person is looking at the top of a tree from a distance of 15 meters. If the an

A person is looking at the top of a tree from a distance of 15 meters. If the angle of elevation is 30 degrees, what is the height of the tree?

A person is looking at the top of a tree from a distance of 15 meters. If the angle of elevation is 30 degrees, what is the height of the tree?

Step 1: Understand the problem. We need to find the height of a tree when looking at it from a distance of 15 meters and at an angle of elevation of 30 degrees.
Step 2: Recall the relationship between the height of the tree, the distance from the tree, and the angle of elevation. We can use the tangent function: tan(angle) = height / distance.
Step 3: Rearrange the formula to find the height: height = distance * tan(angle).
Step 4: Plug in the values. The distance is 15 meters and the angle is 30 degrees. We need to find tan(30 degrees).
Step 5: Know that tan(30 degrees) is equal to 1/√3.
Step 6: Substitute tan(30 degrees) into the formula: height = 15 * (1/√3).
Step 7: Calculate the height: height = 15/√3.
Step 8: To express the height in a simpler form, multiply the numerator and denominator by √3: height = (15√3)/3 = 5√3 meters.
Step 9: Conclude that the height of the tree is 5√3 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.