Expert: Scott A Wilson - 11/7/2009

Question
QUESTION: I need help with this word problem, please:

A building contractor is planning to use a ladder to reach a window. If an 18-ft ladder leans against the building, with an angle of elevation of 63, how far up the building will the ladder reach? Will the contractor be able to reach a window 16 feet above ground level? Show work.



ANSWER: The ladder is the hypoteneuse of a right triangle.  The ground is the horizontal edge and the building is the vertical edge.  The base angle is 63° and the side is 18'.

The height h is given by sin(63°) = h/18'.

This says that h = 18•sin(63°).

Now sin(63°) = 2.1991, so 18•sin(63°) =  39.6'.

---------- FOLLOW-UP ----------

QUESTION: Thank you!  Now, can you tell me if the contractor be able to reach a window 16 feet above ground level?  

Answer
Most the time if the ladder reaches the bottom of the window that's OK, so if the ladder is 18' and the window is 16', then the space on the ground will be the other let in that right triangle where 18 is the hypotenuse and 16 is the leg given.

We know that 16² + X² = 18², or 256 + X² = 324, so X² = 324 - 256 = 68,
so X is at least 8 feet, which is more than enough space.