From a point on the ground, the angle of elevation to the top of a tower is 45 degrees. If the point is 10 meters away from the base of the tower, what is the height of the tower?
Practice Questions
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Q1
From a point on the ground, the angle of elevation to the top of a tower is 45 degrees. If the point is 10 meters away from the base of the tower, what is the height of the tower?
10 meters
15 meters
20 meters
25 meters
Height = distance * tan(45) = 10 * 1 = 10 meters
Questions & Step-by-step Solutions
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Q
Q: From a point on the ground, the angle of elevation to the top of a tower is 45 degrees. If the point is 10 meters away from the base of the tower, what is the height of the tower?
Step 1: Understand the problem. We have a tower and a point on the ground that is 10 meters away from the base of the tower.
Step 2: Identify the angle of elevation. The angle from the point on the ground to the top of the tower is 45 degrees.
Step 3: Recall the relationship in a right triangle. The height of the tower (opposite side) and the distance from the point to the base of the tower (adjacent side) form a right triangle.
Step 4: Use the tangent function. The tangent of an angle in a right triangle is the ratio of the opposite side to the adjacent side. For 45 degrees, tan(45) = 1.
Step 5: Set up the equation. Height of the tower = distance from the point to the base of the tower * tan(45 degrees).
