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)?

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Q: 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)?

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

Steps: 7

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.