A tree is 30 meters tall. If the angle of elevation from a point 40 meters away
Practice Questions
Q1
A tree is 30 meters tall. If the angle of elevation from a point 40 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 30 meters tall. If the angle of elevation from a point 40 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 30 meters.
Step 2: Identify the distance from the point to the base of the tree, which is 40 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 (30 meters) and the adjacent side is the distance from the point to the tree (40 meters).
Step 5: Substitute the values into the formula: tan(θ) = 30 / 40.
Step 6: Simplify the fraction: 30 / 40 = 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.
