A 9ft. Ladder is leaning against a wall and make a 50 degree angle with the ground. How far is the ladder from the base of the wall.
distance=9cos50
To find out how far the ladder is from the base of the wall, we can use trigonometry, specifically the sine function. Here's how you can determine the distance:
1. Identify the relevant angle: In this case, the angle between the ladder and the ground is given as 50 degrees.
2. Find the opposite side: The height of the wall, which is perpendicular to the ground and opposite to the angle, represents the opposite side. We'll call this distance "h" for simplicity.
3. Use the sine function: The sine of an angle is defined as the ratio of the length of the opposite side to the length of the hypotenuse. The hypotenuse is the ladder's length, which is 9ft.
So, we have: sin(50°) = h/9ft
4. Rearrange the equation: To find "h," we can isolate it by multiplying both sides of the equation by 9ft:
h = 9ft * sin(50°)
5. Calculate the value: Using a calculator, find the sine of 50 degrees, then multiply it by 9ft to get the distance from the base of the wall:
h ≈ 9ft * sin(50°) ≈ 6.88ft (rounded to two decimal places)
Therefore, the ladder is approximately 6.88 feet away from the base of the wall.