A ladder 12 m long is propped up against a building at an angle of 15°. How far up the wall does the ladder go?
Its been 6 whole years and im back
To find out how far up the wall the ladder goes, we can use trigonometry. The side of the ladder against the wall is the adjacent side, and the hypotenuse is the length of the ladder. We need to find the length of the opposite side, which represents how far up the wall the ladder reaches.
Let's use the formula:
Sin(angle) = Opposite / Hypotenuse.
Here, the angle is 15°, and the hypotenuse is 12 m.
Sin(15°) = Opposite / 12.
To find the length of the opposite side, we can rearrange the equation:
Opposite = Sin(15°) * 12.
Using a calculator, we find:
Sin(15°) ≈ 0.2588.
Opposite ≈ 0.2588 * 12.
Therefore, the ladder goes approximately 3.10 meters up the wall.
To find how far up the wall the ladder goes, we can use trigonometry and the given information.
Let's assume that the distance up the wall is represented by 'x'.
In this scenario, we have a right triangle formed by the ladder, the wall, and the ground. The length of the ladder is the hypotenuse, and the angle between the ground and the ladder is 15°.
Using trigonometry, we can use the sine function to relate the angle and the sides of this right triangle.
The sine of an angle is equal to the opposite side divided by the hypotenuse. In this case, the opposite side is 'x', and the hypotenuse is 12 m.
So, we have:
sin(15°) = x / 12
Now, we can solve the equation for 'x':
x = 12 * sin(15°)
To find the value of sin(15°), you can either use a scientific calculator or an online trigonometric calculator.
Using the calculator, we find that sin(15°) ≈ 0.2588.
Now, substituting this value into the equation, we get:
x = 12 * 0.2588
x ≈ 3.106 m
Therefore, the ladder goes approximately 3.106 meters up the wall.
If you draw the figure, you'll have a right triangle with the ladder as the hypotenuse.
Let x = how far up the wall the ladder goes
We can use sines:
sin (angle) = opposite / hypotenuse
sin (15°) = x / 12
x = 12 sin (15°)
x = ?
Units in meters. Hope this helps~ `u`