Tom wants to reach a second floor window on a house that is 20 feet above ground. if he must put the ladder at a 70 degree angle to the ground, how long must the ladder be?

Picture a right triangle whose hypotenuse is of unknown length.  Let's call that length L.  The triangle side opposite the 70 degree angle is then 20 feet.  I'd suggest you actually draw this triangle.

Then, using the definition of the sine function,

sin 70 deg = opp / hyp = (20 ft) / L.   Transforming this equation, L sin 70 deg = 20 ft.  Solving for L:

L = (20 ft) / (sin 70 deg) = 21.28 ft 

The ladder length must be 21.28 ft.

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