SOLUTION: The base of a ladder is 4 horizontal feet from the wall where its top rests. The slope of the line made by the ladder is 3.0. What is the vertical height of the top of the ladder?

Question 757719: The base of a ladder is 4 horizontal feet from the wall where its top rests. The slope of the line made by the ladder is 3.0. What is the vertical height of the top of the ladder? (Assume that the positive direction points from the base of the ladder toward the wall.)
Found 2 solutions by stanbon, solver91311:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The base of a ladder is 4 horizontal feet from the wall where its top rests. The slope of the line made by the ladder is 3.0. What is the vertical height of the top of the ladder? (Assume that the positive direction points from the base of the ladder toward the wall.)
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Draw the picture:
You have a right triangle with base = 4 feet,
Let the vertical height be "h":
Equation:
slope = rise/run = 3
h/4 = 3
h = 12 ft
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Cheers,
Stan H.
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Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Plot your problem on a set of coordinate axes, assuming without loss of generality, that the vertical wall is co-incident with the positive -axis, the ground is co-incident with the -axis, and the origin, is the point of intersection with the wall and the ground.

Given that the positive direction in the -axis is from the base of the ladder toward the wall, the base of the ladder must be at the point . You are given that the slope of the ladder is 3.

Use the point-slope form of an equation of a line to derive an equation of the line that contains the line segment representing the ladder.

where are the coordinates of the given point and is the given slope.

Since the ladder touches the wall at some point , substitute zero for in your equation and solve for the value of which will be the vertical height of the top of the ladder.

John

Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it

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