a ladder of length 3.5m rests against a vertical wall and makes an angle of 40 degrees with the floor. How far up the wall does the ladder reach?
sin40 = h/3.5.
h = 3.5*sin40.
Well, if I were a ladder, I'd probably ask, "Can someone help me reach my goals? I'm feeling a little inclined!" But in this case, we can use some mathematics to find the height the ladder reaches on the wall.
We have a right triangle formed by the ladder, the wall, and the floor. The ladder acts as the hypotenuse, while the height we're trying to find is the opposite side to the angle of 40 degrees.
Using the sine function, we can say: sin(40 degrees) = opposite / hypotenuse.
Plugging in the values, we have: sin(40 degrees) = height / 3.5m.
Solving for the height, we get: height = sin(40 degrees) * 3.5m.
Calculating this, we find that the ladder reaches approximately 2.24m up the wall. So, it's like the ladder is saying, "I've got your back, wall! Let me lift your spirits up by 2.24m!"
To find out how far up the wall the ladder reaches, we can use trigonometric ratios. The most suitable ratio for this problem is the sine ratio.
Step 1: Identify the information given in the problem:
- Length of the ladder: 3.5m
- Angle between the ladder and the floor: 40 degrees
Step 2: Use the sine ratio (sin) to calculate the height.
sin(angle) = opposite/hypotenuse
In this case, the height of the wall represents the opposite side, and the ladder represents the hypotenuse.
Step 3: Substitute the values into the trigonometric equation:
sin(40 degrees) = height/3.5m
Step 4: Solve the equation for the height:
height = sin(40 degrees) * 3.5m
Step 5: Calculate the height:
Using a calculator, find the sine of 40 degrees, which is approximately 0.6428.
height = 0.6418 * 3.5m
height ≈ 2.2495m
Therefore, the ladder reaches approximately 2.2495 meters up the wall.
To determine how far up the wall the ladder reaches, we can use trigonometry.
Let's denote the length of the ladder as 'l', the height it reaches on the wall as 'h', and the angle it forms with the floor as 'θ'.
In this case, we have the length of the ladder, l = 3.5 meters, and the angle θ = 40 degrees.
To find the height (h), we can use the trigonometric function sine (sin). The sine of an angle is equal to the ratio of the length of the side opposite the angle to the length of the hypotenuse.
So, we can use the formula: sin(θ) = opposite/hypotenuse.
In this case, the height of the ladder on the wall (h) is the opposite side, and the length of the ladder (l) is the hypotenuse.
Therefore, we can rearrange the formula to solve for h:
h = l * sin(θ)
Now, let's substitute the given values:
h = 3.5 * sin(40°)
Using a calculator, we can evaluate sin(40°) and find that it is approximately 0.6428.
Now, we can substitute this value into the equation:
h = 3.5 * 0.6428
Calculating this, we find that the ladder reaches approximately 2.2498 meters up the wall.
the ladder is the HYPOTENUSE
the wall is OPPOSITE the 40º angle