A building is 20 meters tall. If the angle of elevation from a point 10 meters a

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Question: A building is 20 meters tall. If the angle of elevation from a point 10 meters away from the base of the building is θ, what is tan(θ)?

Options:

Correct Answer: 2

Solution:

tan(θ) = height/distance = 20/10 = 2.

A building is 20 meters tall. If the angle of elevation from a point 10 meters away from the base of the building is θ, what is tan(θ)?

A building is 20 meters tall. If the angle of elevation from a point 10 meters away from the base of the building is θ, what is tan(θ)?

Step 1: Identify the height of the building, which is 20 meters.
Step 2: Identify the distance from the point to the base of the building, which is 10 meters.
Step 3: Recall the definition of tangent in a right triangle: tan(θ) = opposite side / adjacent side.
Step 4: In this scenario, the 'opposite side' is the height of the building (20 meters) and the 'adjacent side' is the distance from the point to the building (10 meters).
Step 5: Substitute the values into the formula: tan(θ) = 20 meters / 10 meters.
Step 6: Simplify the fraction: 20 / 10 = 2.
Step 7: Conclude that tan(θ) = 2.

Trigonometric Ratios – Understanding the relationship between the angles and sides of a right triangle, specifically the tangent function which is the ratio of the opposite side to the adjacent side.