Q: From a point 80 meters away from the base of a tower, the angle of elevation to the top of the tower is 30 degrees. What is the height of the tower?
Step 1: Understand the problem. You have a tower and you are standing 80 meters away from its base.
Step 2: Identify the angle of elevation. The angle from your line of sight to the top of the tower is 30 degrees.
Step 3: Use the tangent function. The tangent of an angle in a right triangle is the opposite side (height of the tower) divided by the adjacent side (distance from the tower).
Step 4: Write the formula. Height = distance * tan(angle). Here, distance = 80 meters and angle = 30 degrees.
Step 5: Find tan(30 degrees). The value of tan(30 degrees) is 1/√3 or approximately 0.577.
Step 6: Substitute the values into the formula. Height = 80 * (1/√3).
Step 7: Calculate the height. Height = 80 / 1.732, which is approximately 46.19 meters.
