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?
Practice Questions
1 question
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
Using tan(60°) = height/distance, we have √3 = 30/distance. Therefore, distance = 30/√3 m.
Questions & Step-by-step Solutions
1 item
Q
Q: 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?
Solution: Using tan(60°) = height/distance, we have √3 = 30/distance. Therefore, distance = 30/√3 m.
Steps: 9
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.
