A tower is standing on a horizontal ground. The angle of elevation of the top of
Practice Questions
Q1
A tower is standing on a horizontal ground. The angle of elevation of the top of the tower from a point on the ground is 30 degrees. If the height of the tower is 50 meters, how far is the point from the base of the tower?
50√3 m
100 m
50 m
100√3 m
Questions & Step-by-Step Solutions
A tower is standing on a horizontal ground. The angle of elevation of the top of the tower from a point on the ground is 30 degrees. If the height of the tower is 50 meters, how far is the point from the base of the tower?
Step 1: Understand the problem. We have a tower that is 50 meters tall and we want to find out how far a point on the ground is from the base of the tower when the angle of elevation to the top of the tower is 30 degrees.
Step 2: Recall the relationship between the height of the tower, the distance from the point to the base of the tower, and the angle of elevation. We can use the tangent function: tan(angle) = opposite/adjacent.
Step 3: Identify the 'opposite' side and the 'adjacent' side. The 'opposite' side is the height of the tower (50 meters) and the 'adjacent' side is the distance we want to find.
Step 4: Write the equation using the tangent function: tan(30°) = height/distance. This means tan(30°) = 50/distance.
Step 5: We know that tan(30°) is equal to 1/√3. So we can rewrite the equation: 1/√3 = 50/distance.
Step 6: Rearrange the equation to solve for distance: distance = height/tan(30°).
Step 7: Substitute the height (50 meters) into the equation: distance = 50/(1/√3).
Step 9: Calculate the final answer: distance = 50√3 meters.
Trigonometry – The problem involves using the tangent function to relate the height of the tower to the distance from the base using the angle of elevation.
Right Triangle Properties – Understanding the properties of right triangles is essential, as the scenario describes a right triangle formed by the tower, the ground, and the line of sight.
