From the top of a 100 m high building, the angle of depression to a point on the
Practice Questions
Q1
From the top of a 100 m high building, the angle of depression to a point on the ground is 45 degrees. How far is the point from the base of the building? (2020)
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Questions & Step-by-Step Solutions
From the top of a 100 m high building, the angle of depression to a point on the ground is 45 degrees. How far is the point from the base of the building? (2020)
Step 1: Understand the problem. We have a building that is 100 meters tall.
Step 2: Identify the angle of depression. It is given as 45 degrees.
Step 3: Visualize the situation. Draw a right triangle where the height of the building is one side (100 m) and the distance from the base of the building to the point on the ground is the other side.
Step 4: Recall the relationship in a right triangle. The tangent of an angle is equal to the opposite side divided by the adjacent side.
Step 5: Set up the formula. For our triangle, tan(45 degrees) = height / distance.
Step 6: Substitute the known values into the formula. We have tan(45 degrees) = 100 m / distance.
Step 7: Calculate tan(45 degrees). It is equal to 1.
Step 8: Rewrite the equation. Now we have 1 = 100 m / distance.
Step 9: Solve for distance. Multiply both sides by distance to get distance = 100 m.
Step 10: Conclude that the distance from the base of the building to the point on the ground is 100 meters.
Angle of Depression – The angle formed by a horizontal line and the line of sight to an object below the horizontal line.
Tangent Function – In a right triangle, the tangent of an angle is the ratio of the opposite side to the adjacent side.
Right Triangle Properties – Understanding the relationship between the sides and angles in a right triangle is crucial for solving problems involving heights and distances.
