Math (degress, tagine, sin)?

A gutter cleaner wants to reach a gutter 40 ft above the

ground. Find the length of the shortest ladder that can be

used if the steepest angle at which it can be leaned against

the house has measure 75掳.



The answer to this one is 42' ladder but can you explain how this is the answer.Math (degress, tagine, sin)?
Draw the ladder and the house as a right triangle. The vertical side is 40'. The angle at the bottom of the triangle is 75掳. The wall of the house is the opposite side; the ladder is the hypotenuse.



sin 75掳 = Opp/Hyp



Hyp = Opp/sin 75掳 = 40/0.966 = 41.1 feet

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