Me! 1. joshua has a ladder that is 17ft long. he wants to lean the ladder against a vertical wall so that the top of the ladder is 16.5ftabove the ground. for safety reasons, he wants the angle the ladder makes with the ground to be no greater than 70°. will the ladder be safe at this height? show your work. make sure you show your work.

not safe

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you of the relationship between an angle and the ratio of side opposite to hypotenuse:

Sin = Opposite/Hypotenuse

You have the ratio of lengths and you want to find the angle. You use the inverse sine function (arcsin, or sin⁻¹) for this purpose.

sin(angle with ground) = (16.5 ft)/(17 ft) = 33/34

angle with ground = arcsin(33/34) ≈ 76.1°

This angle is greater than the angle of 70° recommended as a maximum. The ladder will not be safe at this height.

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A calculator does all the work. You just need to make sure it is in degrees mode.

step-by-step explanation: