A building casts a shadow of 10 meters when the angle of elevation of the sun is 30 degrees. What is the height of the building?

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Q: A building casts a shadow of 10 meters when the angle of elevation of the sun is 30 degrees. What is the height of the building?

Solution: Height = shadow * tan(angle) = 10 * √3 = 5√3 meters.

Steps: 9

Step 1: Understand that the angle of elevation is the angle between the ground and the line from the top of the building to the sun.
Step 2: Recognize that the shadow of the building and the height of the building form a right triangle with the ground.
Step 3: Identify the angle of elevation of the sun, which is given as 30 degrees.
Step 4: Use the tangent function, which relates the height of the building to the length of the shadow: tan(angle) = height / shadow.
Step 5: Rearrange the formula to find the height: height = shadow * tan(angle).
Step 6: Substitute the values into the formula: height = 10 * tan(30 degrees).
Step 7: Calculate tan(30 degrees), which is equal to 1/√3 or √3/3.
Step 8: Multiply: height = 10 * (1/√3) = 10/√3. To simplify, multiply by √3/√3: height = (10√3)/3.
Step 9: The final answer can also be expressed as approximately 5√3 meters.