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?
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 meters, how far is the point from the base of the tower?
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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 meters, 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 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.
