From a point on the ground, the angle of elevation to the top of a tower is 60 d
Practice Questions
Q1
From a point on the ground, the angle of elevation to the top of a tower is 60 degrees. If the tower is 30 m high, how far is the point from the base of the tower?
15 m
30 m
20 m
10 m
Questions & Step-by-Step Solutions
From a point on the ground, the angle of elevation to the top of a tower is 60 degrees. If the tower is 30 m high, how far is the point from the base of the tower?
Correct Answer: 10√3 m
Step 1: Understand the problem. We have a tower that is 30 meters high and we want to find out how far away a point on the ground is from the base of the tower.
Step 2: Identify the angle of elevation. The angle of elevation from the point on the ground to the top of the tower is 60 degrees.
Step 3: Use the tangent function. In a right triangle, the tangent of an angle is equal to the opposite side (height of the tower) divided by the adjacent side (distance from the tower).
Step 4: Write the equation using the tangent function. We have tan(60°) = height/distance, which means tan(60°) = 30/distance.
Step 5: Know the value of tan(60°). The value of tan(60°) is √3.
Step 6: Substitute the value into the equation. Now we have √3 = 30/distance.
Step 7: Rearrange the equation to find distance. Multiply both sides by distance: distance * √3 = 30.
Step 8: Solve for distance. Divide both sides by √3: distance = 30/√3.
Step 9: Simplify if needed. This is the final answer for the distance from the point to the base of the tower.
Trigonometric Ratios – The question tests the understanding of the tangent function in right triangles, specifically how to relate the angle of elevation to the height and distance from the base.
Angle of Elevation – It assesses the ability to interpret the angle of elevation in a real-world context and apply it to find distances.
Right Triangle Properties – The problem involves recognizing the relationship between the sides of a right triangle formed by the tower, the ground, and the line of sight.
