Math problem help!!

Question

A ladder is 4.0m long. The bottom of the ladder is placed 0.8m from the wall l. How high up on the wall will the ladder reach?

please show work to help me! Thanks

Answer 1

Let's draw the problem. The ladder is placed against the wall, the length of the ladder (c) is 4 m.

The distance of the ladder from the wall (a) = 0.8 m. How high up the wall (b) is what we want to find.

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b | \ c

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| \ <----- ladder

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a

From the drawing we see we have created a right triangle.

To solve this problem we will be using the Pythagorean Theorem for right triangles:

a**2 + b**2 = c**2 where a and b are the legs of the right triangle and c is the hypotenuse.

The ladder will be leaning against the wall and will form the hypotenuse of the right triangle (c) and is of length 4 meters.

The distance of the ladder from the wall (0.8 meters) will form one of the legs of the right triangle (a).

How high the ladder is up the wall, will form the other leg (b) of the right triangle.

Substituting our values for a and c in to our formula above we get:

0.8**2 + b**2 = 4**2

So that b**2 = 4**2 - 0.8**2

b = 15.36 and b = 3,919 feet.