A building casts a shadow of 10 meters when the angle of elevation of the sun is

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?

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?

Correct Answer: 5√3 meters

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.

Trigonometry – The problem involves using the tangent function to relate the height of the building to the length of the shadow and the angle of elevation of the sun.
Angle of Elevation – Understanding how the angle of elevation affects the relationship between the height of an object and the length of its shadow.