From a point on the ground, the angle of elevation to the top of a tower is 30 d
Practice Questions
Q1
From a point on the ground, the angle of elevation to the top of a tower is 30 degrees. If the tower is 10 meters tall, how far is the point from the base of the tower?
5√3 meters
10 meters
15 meters
20 meters
Questions & Step-by-Step Solutions
From a point on the ground, the angle of elevation to the top of a tower is 30 degrees. If the tower is 10 meters tall, how far is the point from the base of the tower?
Step 1: Understand the problem. We have a tower that is 10 meters tall and we want to find out how far away we are from the base of the tower.
Step 2: Identify the angle of elevation. The angle of elevation 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 base).
Step 4: Write the formula. We can express this as: tan(30 degrees) = height / distance.
Step 5: Plug in the values. We know the height is 10 meters, so we write: tan(30 degrees) = 10 / distance.
Step 6: Find the value of tan(30 degrees). The value of tan(30 degrees) is 1/√3.
Step 7: Set up the equation. Now we have: 1/√3 = 10 / distance.
Step 8: Rearrange the equation to solve for distance. Multiply both sides by distance and then by √3: distance = 10 / (1/√3).
Step 9: Simplify the equation. This gives us distance = 10 * √3.
Step 10: Calculate the final answer. The distance from the point to the base of the tower is 10√3 meters.
Trigonometry – The problem involves using the tangent function to relate the height of the tower to the distance from the base.
Angle of Elevation – Understanding how the angle of elevation relates to the height and distance in a right triangle.
