SOLUTION: kayla wants to know how high a 15 inch piece of wood will reach on a nightstand she is building if its angle of elevation is 47 degrees.

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Question 1111755: kayla wants to know how high a 15 inch piece of wood will reach on a nightstand she is building if its angle of elevation is 47 degrees.
Found 2 solutions by Alan3354, Theo:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
15*sin(47) inches

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
the wood makes an angle of 47 degrees with the floor.

this forms a right triangle, where the hypotenuse is 15 inches and the angle between the floor and the piece of wood is 47 degrees and the height is opposite the 47 degree angle.

sine (47 degrees) = opposite / hypotenuse = height / 15.

solve for height to get:

height = 15 * sine (47 degrees).

this results in height = 10.97030552 inches.

here's my diagram:

$$$

the nightstand is the horizontal line through point A.

the piece of wood is the line segment AC.

the height of the nightstand is the line segment AB

the angle of inclination if angle ACB.

the formula used is shown in the diagram.

the height of the table is represented by x whihc is equal to 10.970305552 inches.

rounded to 2 decimal places, the height is equal to 10.97 inches.