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 m, how far is the point from the base of the tower?
Practice Questions
1 question
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 m, how far is the point from the base of the tower?
10 m
5 m
15 m
20 m
Using tan(30°) = height/distance, we have 1/√3 = 10√3/distance. Therefore, distance = 10√3 * √3 = 30 m.
Questions & Step-by-step Solutions
1 item
Q
Q: 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 m, how far is the point from the base of the tower?
Solution: Using tan(30°) = height/distance, we have 1/√3 = 10√3/distance. Therefore, distance = 10√3 * √3 = 30 m.
Steps: 10
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 base).
Step 5: Write the formula using the tangent function: tan(30°) = height / distance.
Step 6: Substitute the known values into the formula: tan(30°) = 10√3 / distance.
Step 7: Know that tan(30°) is equal to 1/√3.
Step 8: Set up the equation: 1/√3 = 10√3 / distance.
Step 9: Rearrange the equation to solve for distance: distance = 10√3 * √3.
