From a point on the ground, the angle of elevation to the top of a hill is 45 de
Practice Questions
Q1
From a point on the ground, the angle of elevation to the top of a hill is 45 degrees. If the height of the hill is 100 m, how far is the point from the base of the hill?
100 m
50 m
200 m
150 m
Questions & Step-by-Step Solutions
From a point on the ground, the angle of elevation to the top of a hill is 45 degrees. If the height of the hill is 100 m, how far is the point from the base of the hill?
Step 1: Understand that the angle of elevation is the angle formed between the horizontal line from the point on the ground and the line of sight to the top of the hill.
Step 2: Identify that the height of the hill is given as 100 meters.
Step 3: Recognize that the angle of elevation is 45 degrees.
Step 4: Recall the trigonometric function tangent (tan), which relates the angle of a right triangle to the opposite side (height) and the adjacent side (distance).
Step 5: Write the formula for tangent: tan(angle) = opposite/adjacent.
Step 6: Substitute the known values into the formula: tan(45°) = height/distance.
Step 7: Since tan(45°) equals 1, rewrite the equation as 1 = 100/distance.
Step 8: Rearrange the equation to find distance: distance = height/tan(45°).
Step 9: Substitute the height into the equation: distance = 100/1.
Step 10: Calculate the distance: distance = 100 meters.
Trigonometry – The problem involves using the tangent function to relate the angle of elevation, height, and distance.
Angle of Elevation – Understanding how the angle of elevation relates to the height of an object and the distance from the observer.
