A 12 foot ladder leaning at a 75 degree angle how far up the wall does the ladder reach
sin 75 degrees = x/12
find the sin of 75 and multiply by 12
12
To find out how far up the wall the ladder reaches, we can use trigonometry.
We know that the ladder forms a right triangle with the wall, where the ladder is the hypotenuse and the distance up the wall is the opposite side.
Since we are given the length of the ladder (12 feet) and the angle it makes with the ground (75 degrees), we can use the sine function to calculate the distance up the wall.
The formula we can use is:
sin(angle) = opposite/hypotenuse
Plugging in the values, we have:
sin(75) = opposite/12
To find the distance up the wall (opposite side), we can rearrange the equation and solve for opposite:
opposite = sin(75) * 12
Now, let's calculate it:
sin(75) ≈ 0.966
opposite ≈ 0.966 * 12 ≈ 11.59 feet
Therefore, the ladder reaches approximately 11.59 feet up the wall.
To determine how far up the wall the ladder reaches, you can use some trigonometry. The ladder, the distance it reaches up the wall, and the ground form a right triangle. The length of the ladder is the hypotenuse of this triangle, and the angle between the ladder and the ground is given as 75 degrees.
To find the distance up the wall, you need to determine the length of the side adjacent to the angle of 75 degrees. In this case, it represents the distance up the wall.
Here's how you can calculate it step by step:
1. Identify the side lengths of the right triangle:
- The length of the ladder (hypotenuse) is 12 feet.
- The side adjacent to the angle of 75 degrees is what we're trying to find (let's call it "x").
- The side opposite to the angle of 75 degrees is the distance on the ground.
2. Use the cosine function:
The cosine of an angle is equal to the adjacent side divided by the hypotenuse.
In this case, cos(75) = x/12.
Rearranging the equation gives: x = 12 * cos(75).
3. Calculate x:
Using a calculator, compute the value of cos(75). Multiply 12 by the cosine of 75 degrees to obtain the distance up the wall.
By following these steps, you'll determine the exact distance up the wall that the ladder reaches.