If a 14-ft ladder leans
against a building, with an angle of elevation of 70°, how far up the building will the ladder
reach?
I believe this requires law of cosines but otherwise I am lost.
nope. Just the definition of the sine:
h/14 = sin 70°
For the law of cosines, you need two sides and their included angle.
To find how far up the building the ladder will reach, we can use trigonometry and the angle of elevation.
Let's label the length of the ladder as "l" and the height up the building as "h".
In this case, we are given the length of the ladder (l = 14 ft) and the angle of elevation (θ = 70°).
We want to find the height up the building (h).
To solve for h, we can use the sine function:
sin(θ) = opposite/hypotenuse
In this case, the opposite side is h (the height up the building) and the hypotenuse is the length of the ladder (l).
So we have:
sin(70°) = h/14
Now, we can solve for h:
h = 14 * sin(70°)
To calculate this using a scientific calculator:
1. Make sure your calculator is in degree mode.
2. Enter 70, then press the sin button.
3. Multiply the result by 14.
By using this method, we can find the height up the building that the ladder will reach.