A man is standing on a hill 80 meters high. If he looks at a point on the ground
Practice Questions
Q1
A man is standing on a hill 80 meters high. If he looks at a point on the ground at an angle of depression of 45 degrees, how far is the point from the base of the hill?
80 meters
40√2 meters
80√2 meters
60 meters
Questions & Step-by-Step Solutions
A man is standing on a hill 80 meters high. If he looks at a point on the ground at an angle of depression of 45 degrees, how far is the point from the base of the hill?
Step 1: Understand that the man is on a hill that is 80 meters high.
Step 2: Know that the angle of depression is the angle between the horizontal line from the man's eyes and the line of sight to the point on the ground.
Step 3: Recognize that an angle of depression of 45 degrees means the line of sight goes down at a 45-degree angle.
Step 4: Use the tangent function, which relates the height of the hill to the distance on the ground. The formula is: Distance = height / tan(angle).
Step 5: Plug in the values: height = 80 meters and angle = 45 degrees. So, Distance = 80 / tan(45°).
Step 6: Calculate tan(45°), which is 1. Therefore, Distance = 80 / 1.
Step 7: Conclude that the distance from the base of the hill to the point on the ground is 80 meters.
Angle of Depression – The angle formed by a horizontal line and the line of sight down to an object below.
Tangent Function – In a right triangle, the tangent of an angle is the ratio of the opposite side to the adjacent side.
Right Triangle Properties – Understanding the relationships between the sides and angles in a right triangle.
