An 18 meter ladder leaning against a building makes a 70 angle with ground. How far up the building does the ladder touch?
To find how far up the building the ladder touches, we can use the trigonometric function cosine.
Cosine relates the adjacent side of a right triangle to the hypotenuse. In this case, the adjacent side represents the distance up the building and the hypotenuse represents the ladder.
Let's call the distance up the building "x". We can set up the following equation using cosine:
cos(70°) = x / 18
To solve for x, we can rearrange the equation:
x = 18 * cos(70°)
Now we can calculate the value of x:
x = 18 * cos(70°)
x ≈ 18 * 0.3420
x ≈ 6.156
Therefore, the ladder touches approximately 6.156 meters up the building.
To find out how far up the building the ladder touches, we can use trigonometry. Specifically, we can use the sine function.
The sine of an angle is defined as the length of the side opposite the angle divided by the length of the hypotenuse. In this case, the opposite side is the height up the building where the ladder touches and the hypotenuse is the length of the ladder.
Let's call the height up the building "h".
Using the given information, we know that the length of the ladder (hypotenuse) is 18 meters and the angle between the ladder and the ground is 70 degrees.
The sine function can be written as sin(angle) = opposite/hypotenuse.
Plugging in the known values, we have sin(70) = h/18.
To find the value of h, we rearrange the equation: h = sin(70) * 18.
Now we can calculate the value of h.
Using a calculator, we find that sin(70) is approximately 0.9397. Multiplying this by 18, we get:
h = 0.9397 * 18.
Calculating this, we find that h is approximately 16.9166.
Therefore, the ladder touches the building approximately 16.92 meters up.
The ladder would end up making a right triangle with the ground and the wall, so that makes it possible to use the sine law because you know the angle across from the ladder.
18/sin 90 = x/sin 70
x = 18*sin 90
= 16.91m