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A building is 20 meters tall. If a person standing 15 meters away from the build

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Question: A building is 20 meters tall. If a person standing 15 meters away from the building sees the top at an angle of elevation of θ, what is sin(θ)?

Options:

  1. 0.8
  2. 0.6
  3. 0.5
  4. 0.75

Correct Answer: 0.8

Solution: 

sin(θ) = height / hypotenuse; hypotenuse = √(20^2 + 15^2) = √625 = 25; sin(θ) = 20/25 = 0.8

A building is 20 meters tall. If a person standing 15 meters away from the build

Practice Questions

Q1
A building is 20 meters tall. If a person standing 15 meters away from the building sees the top at an angle of elevation of θ, what is sin(θ)?
  1. 0.8
  2. 0.6
  3. 0.5
  4. 0.75

Questions & Step-by-Step Solutions

A building is 20 meters tall. If a person standing 15 meters away from the building sees the top at an angle of elevation of θ, what is sin(θ)?
Correct Answer: 0.8
  • Step 1: Identify the height of the building, which is 20 meters.
  • Step 2: Identify the distance from the person to the building, which is 15 meters.
  • Step 3: Recognize that we can form a right triangle where the height of the building is one side (20 meters) and the distance from the person to the building is the other side (15 meters).
  • Step 4: Use the Pythagorean theorem to find the hypotenuse of the triangle. The formula is hypotenuse = √(height² + distance²).
  • Step 5: Calculate the hypotenuse: hypotenuse = √(20² + 15²) = √(400 + 225) = √625 = 25 meters.
  • Step 6: Use the definition of sine in a right triangle, which is sin(θ) = opposite side / hypotenuse. Here, the opposite side is the height of the building (20 meters) and the hypotenuse is 25 meters.
  • Step 7: Calculate sin(θ): sin(θ) = 20 / 25 = 0.8.
  • Trigonometry – Understanding the relationship between the angles and sides of a right triangle, specifically using sine to find the ratio of the opposite side to the hypotenuse.
  • Pythagorean Theorem – Applying the theorem to calculate the hypotenuse of a right triangle formed by the height of the building and the distance from the person to the building.
  • Angle of Elevation – Understanding how to interpret the angle of elevation from a point to the top of an object.
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