If a 50-meter tall building casts a shadow of 25 meters, what is the angle of el

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Question: If a 50-meter tall building casts a shadow of 25 meters, what is the angle of elevation of the sun?

Options:

Correct Answer: 60 degrees

Solution:

Using tan(θ) = height/shadow length, θ = tan^(-1)(50/25) = tan^(-1)(2) = 60 degrees.

If a 50-meter tall building casts a shadow of 25 meters, what is the angle of elevation of the sun?

If a 50-meter tall building casts a shadow of 25 meters, what is the angle of elevation of the sun?

Step 1: Identify the height of the building, which is 50 meters.
Step 2: Identify the length of the shadow, which is 25 meters.
Step 3: Use the formula for the tangent of the angle of elevation (θ): tan(θ) = height / shadow length.
Step 4: Substitute the values into the formula: tan(θ) = 50 / 25.
Step 5: Simplify the fraction: tan(θ) = 2.
Step 6: To find the angle θ, use the inverse tangent function: θ = tan^(-1)(2).
Step 7: Calculate the angle using a calculator: θ = 60 degrees.

Trigonometry – The problem involves using the tangent function to relate the height of the building and the length of its shadow to find the angle of elevation.
Angle of Elevation – Understanding the concept of angle of elevation as the angle formed between the horizontal ground and the line of sight to an object above the ground.