Answer:
Step-by-step explanation:
Slope-intercept form is written in
So, to solve, we must separate y onto one side and make its coefficient one.
Subtract 4x on both sides.
Divide both sides by the coefficient of , which is 3.
Simplify.
Rewrite this equation into standard form by changing the order of and
From the setup of the problem, the "length of the top of the bookcase, measured along the attic ceiling" will be the hypotenuse of a right triangle, the length "AB". We have both the angle between AB and AC and the length of AC (3.24 meters), so we can use trigonometric identities.
The cosine of the 40 degree angle between AB and AC is equivalent to the length of AC divided by the length of AB. Equivalently, we have:
where "h", the hypotenuse, is the length we want. Rearranging the formula to solve for h we have that
which is 4.2295... meters. Converting to centimeters (multiplying by 100) we have that h = 422.95... centimeters, or if we round the value, h = 423 centimeters.