Question: A building is 20 meters tall. If the angle of elevation from a point on the ground 10 meters away from the base of the building is θ, what is tan(θ)?
Options:
2
0.5
1
1.5
Correct Answer: 2
Solution:
tan(θ) = opposite/adjacent = 20/10 = 2.
A building is 20 meters tall. If the angle of elevation from a point on the grou
Practice Questions
Q1
A building is 20 meters tall. If the angle of elevation from a point on the ground 10 meters away from the base of the building is θ, what is tan(θ)?
2
0.5
1
1.5
Questions & Step-by-Step Solutions
A building is 20 meters tall. If the angle of elevation from a point on the ground 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. This is the 'opposite' side of the triangle formed.
Step 2: Identify the distance from the point on the ground to the base of the building, which is 10 meters. This is the 'adjacent' side of the triangle.
Step 3: Recall the definition of the tangent function (tan) in a right triangle: tan(θ) = opposite / adjacent.
Step 4: Substitute the values into the formula: tan(θ) = 20 meters (opposite) / 10 meters (adjacent).
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.
Right Triangle Properties – Recognizing the right triangle formed by the height of the building, the distance from the point to the base, and the line of sight to the top of the building.
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