A tree is 15 meters tall. If the angle of elevation from a point 20 meters away
Practice Questions
Q1
A tree is 15 meters tall. If the angle of elevation from a point 20 meters away from the base of the tree is θ, what is tan(θ)?
0.75
1.25
1.5
2
Questions & Step-by-Step Solutions
A tree is 15 meters tall. If the angle of elevation from a point 20 meters away from the base of the tree is θ, what is tan(θ)?
Correct Answer: 0.75
Step 1: Identify the height of the tree, which is 15 meters.
Step 2: Identify the distance from the point to the base of the tree, which is 20 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 tree (15 meters) and the adjacent side is the distance from the point to the tree (20 meters).
Step 5: Substitute the values into the formula: tan(θ) = 15 / 20.
Step 6: Simplify the fraction: 15 / 20 = 0.75.
Trigonometry – Understanding the relationship between the angles and sides of a right triangle, specifically using the tangent function.
Angle of Elevation – The angle formed by the horizontal line and the line of sight to an object above the horizontal.
