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 50 m, how far is the point from the base of the hill?
25 m
50 m
70 m
100 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 50 m, how far is the point from the base of the hill?
Correct Answer: 50 m
Step 1: Understand that the angle of elevation is the angle formed between the horizontal ground and the line of sight to the top of the hill.
Step 2: Identify that the height of the hill is 50 meters.
Step 3: Recognize that the angle of elevation is 45 degrees.
Step 4: Use the tangent function, which relates the angle of elevation to the height and distance from the base of the hill. The formula is: tan(angle) = height/distance.
Step 5: Substitute the known values into the formula: tan(45°) = height/distance, which becomes tan(45°) = 50/distance.
Step 6: Know that tan(45°) equals 1. So, the equation simplifies to 1 = 50/distance.
Step 7: Rearrange the equation to find the distance: distance = 50/1.
Step 8: Calculate the distance, which equals 50 meters.
Trigonometry – Understanding the relationship between angles and sides in right triangles, specifically using the tangent function.
Angle of Elevation – The angle formed by the line of sight from a point on the ground to the top of an object above the ground.
Right Triangle Properties – Applying properties of right triangles to solve for unknown lengths using trigonometric ratios.
