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chiane · May 14, 2013, 03:04 PM

Wooden plank is leaning against a wall. The bottom of the plank is 3 feet from the wall. Answer each of the following questions, and show your work.
a) Find AC, the approximate length of the plank. Round to the nearest tenth of a foot.
b) Find BC, the height off the ground where board touches the wall. Round to the nearest foot. Show work step by step
Sketch has right angle... 49 degrees... AC is hypotenuse

wallykap · May 14, 2013, 03:42 PM

assume C is point on wall; B is at base of wall; and A is some distance away from wall.

Using this triangle and assuming that angle A = 49 degrees, then
tan A = BC / 3; and cos A = 3 / AC.

Get a value for BC and AC by solving above using 49 degrees.

you could check answers using Pythagorean theorem and 3 for third side of triangle.

wallykap · May 14, 2013, 03:46 PM

my guess without a calculator would be AC = 4.3 feet and BC = 3.1 feet; how close is my guess??

chiane · May 16, 2013, 02:56 AM

AC = 4.57 BC= 3.45 I used sin for BC instead of tan A... am I right ?

wallykap · May 16, 2013, 04:56 PM

Originally Posted by chiane

AC = 4.57 BC= 3.45 I used sin for BC instead of tan A ...am I right ?

Not to be picky, but math is picky... be aware that "test" asked for answer to nearest foot / tenth of foot. I am pretty sure that your answers should be accurate. Don't be afraid to ask questions throughout life - learning is power.