1. joshua has a ladder that is 12 ft long. he wants to lean the ladder against a vertical wall so that the top of the ladder is 11.8 ft above the ground. for safety reasons, he wants the angle the ladder makes with the ground to be no greater than 75°. will the ladder be safe at this height?

So we'll use trig to solve this because it's a right triangle. The hypotenuse is the ladder (h) and the two smaller sides are the ground and the vertical wall (w).
That angle ladder makes with the ground = €
SOH: sin € = opposite/hypotenuse


No the ladder won't be safe!!!

Now let's make it safe:
The ladder's length (w) is constant, so stays 12
So now let's ask in an inequality what height will be safe (75° or less)


what does that mean?? well as long as you put the ladder against the wall so that the height from ground to top of the ladder is < 11.6 ft!!

Hope that helps! :-D

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