Question: A tree is 15 meters tall. If the angle of elevation from a point on the ground 20 meters away from the base of the tree is θ, what is tan(θ)?
Options:
0.75
0.6
0.5
0.8
Correct Answer: 0.75
Solution:
tan(θ) = height/base = 15/20 = 0.75.
A tree is 15 meters tall. If the angle of elevation from a point on the ground 2
Practice Questions
Q1
A tree is 15 meters tall. If the angle of elevation from a point on the ground 20 meters away from the base of the tree is θ, what is tan(θ)?
0.75
0.6
0.5
0.8
Questions & Step-by-Step Solutions
A tree is 15 meters tall. If the angle of elevation from a point on the ground 20 meters away from the base of the tree is θ, what is tan(θ)?
Step 1: Identify the height of the tree, which is 15 meters.
Step 2: Identify the distance from the point on the ground to the base of the tree, which is 20 meters.
Step 3: Understand that tan(θ) is the ratio of the height of the tree to the distance from the tree.
Step 4: Use the formula for tan(θ): tan(θ) = height / base.
Step 5: Substitute the values into the formula: tan(θ) = 15 / 20.
Step 6: Simplify the fraction: 15 / 20 = 0.75.
Trigonometric Ratios – Understanding the relationship between the angles and sides of a right triangle, specifically using the tangent function.
Right Triangle Properties – Applying the properties of right triangles to solve for unknown angles or sides using given measurements.
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