From a point on the ground, the angle of elevation to the top of a tower is 45 d
Practice Questions
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
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25 meters
Questions & Step-by-Step Solutions
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?
Correct Answer: 10 meters
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).
Trigonometry – The problem involves using the tangent function to relate the angle of elevation to the height of the tower and the distance from the base.
Angle of Elevation – Understanding that the angle of elevation is measured from the horizontal line up to the line of sight to the top of the tower.
Right Triangle Properties – The scenario can be visualized as a right triangle where the height of the tower is the opposite side, the distance from the tower is the adjacent side, and the angle of elevation is given.
