A man is 40 meters away from a building. If he looks up at an angle of 45° to se

₹0.0

Question: A man is 40 meters away from a building. If he looks up at an angle of 45° to see the top of the building, how tall is the building?

Options:

Correct Answer: 40 meters

Solution:

Using tan(45°) = height/40, height = 40 * tan(45°) = 40 meters.

A man is 40 meters away from a building. If he looks up at an angle of 45° to see the top of the building, how tall is the building?

A man is 40 meters away from a building. If he looks up at an angle of 45° to see the top of the building, how tall is the building?

Step 1: Understand that the man is looking up at an angle of 45° from a distance of 40 meters from the building.
Step 2: Recall that the tangent of an angle in a right triangle is the ratio of the opposite side (height of the building) to the adjacent side (distance from the building).
Step 3: Write the formula for tangent: tan(angle) = opposite/adjacent.
Step 4: Substitute the known values into the formula: tan(45°) = height/40.
Step 5: Since tan(45°) equals 1, the equation simplifies to: 1 = height/40.
Step 6: To find the height, multiply both sides by 40: height = 40 * 1.
Step 7: Calculate the height: height = 40 meters.

Trigonometry – The problem involves using the tangent function to relate the angle of elevation to the height of the building and the distance from it.
Right Triangle Properties – Understanding the properties of right triangles, specifically how to apply the tangent ratio in a right triangle scenario.