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 10√3 meters, how far is the point from the base of the tower?
10 m
20 m
30 m
40 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 10√3 meters, how far is the point from the base of the tower?
Correct Answer: 30 m
Step 1: Understand the problem. We have a tower and we want to find out how far a point on the ground is from the base of the tower.
Step 2: Identify the height of the tower. The height is given as 10√3 meters.
Step 3: Identify the angle of elevation. The angle of elevation from the point on the ground to the top of the tower is 30 degrees.
Step 4: Recall the tangent function. The tangent of an angle in a right triangle is the ratio of the opposite side (height of the tower) to the adjacent side (distance from the tower).
Step 5: Write the formula for tangent. For our case, tan(30°) = height / distance.
Step 6: Substitute the known values into the formula. We know tan(30°) = 1/√3 and height = 10√3, so we have 1/√3 = 10√3 / distance.
Step 7: Rearrange the equation to solve for distance. Multiply both sides by distance to get distance * (1/√3) = 10√3.
Step 8: Multiply both sides by √3 to isolate distance. This gives us distance = 10√3 * √3.
Step 9: Simplify the right side. Since √3 * √3 = 3, we have distance = 10 * 3 = 30 meters.
Step 10: Conclude that the distance from the point to the base of the tower is 30 meters.
Trigonometry – The question tests the understanding of the tangent function in right triangles, specifically how to relate the height of an object to the distance from it using angles of elevation.
Angle of Elevation – It assesses the ability to interpret the angle of elevation and apply it to find distances in a real-world context.
