A ladder leans against a wall making an angle of 60 degrees with the ground. If
Practice Questions
Q1
A ladder leans against a wall making an angle of 60 degrees with the ground. If the foot of the ladder is 5 meters away from the wall, what is the height of the ladder on the wall?
5√3 meters
10 meters
5 meters
10√3 meters
Questions & Step-by-Step Solutions
A ladder leans against a wall making an angle of 60 degrees with the ground. If the foot of the ladder is 5 meters away from the wall, what is the height of the ladder on the wall?
Step 1: Understand the problem. We have a ladder leaning against a wall, forming a 60-degree angle with the ground.
Step 2: Identify the distance from the foot of the ladder to the wall. This distance is given as 5 meters.
Step 3: Recognize that we can use trigonometry to find the height of the ladder on the wall. The height corresponds to the opposite side of the triangle formed by the ladder, the wall, and the ground.
Step 4: Use the sine function, which relates the angle to the opposite side and the hypotenuse. The formula is: sin(angle) = opposite / hypotenuse.
Step 5: In our case, the angle is 60 degrees, and the distance from the wall (5 meters) is the adjacent side. We need to find the height (opposite side).
Step 6: Use the cosine function to find the length of the ladder (hypotenuse). cos(60 degrees) = adjacent / hypotenuse. Since cos(60 degrees) = 0.5, we can set up the equation: 0.5 = 5 / hypotenuse.
Step 7: Solve for the hypotenuse: hypotenuse = 5 / 0.5 = 10 meters.
Step 8: Now, use the sine function to find the height: sin(60 degrees) = height / hypotenuse. Since sin(60 degrees) = √3 / 2, we can set up the equation: √3 / 2 = height / 10.
Trigonometry – The problem involves using trigonometric functions to find the height of the ladder based on the angle and distance from the wall.
Right Triangle Properties – The scenario describes a right triangle formed by the ladder, the wall, and the ground, where the angle and one side length are known.
Sine Function – The height can be calculated using the sine function, where height = hypotenuse * sin(angle).
