A painter places an 8.5 ft ladder against a wall. The bottom of the ladder is 4 ft from the base of the wall. How high up the wall does the ladder reach? (hint: round to the nearest tenth)
a^2 + b^2 = c^2
4^2 + b^2 = 8.5^2
16 + b^2 = 72.25
b^2 = 56.25
b = 7.5 feet
It's 7.5 not 8 ft?
The square root of 56.25 = 7.5. That answer is to the nearest tenth.
Very very unsafe placement of a ladder.
a.
3 ft
c.
7.5 ft
b.
16 ft
d.
11.6 ft
To find out how high up the wall the ladder reaches, we need to use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this case, the ladder forms the hypotenuse of a right triangle, with one side measuring 4 ft (the distance from the base of the wall to the bottom of the ladder). Let's call the height up the wall that the ladder reaches "h".
So, using the Pythagorean theorem, we have:
h^2 + 4^2 = 8.5^2
Simplifying this equation, we get:
h^2 + 16 = 72.25
Subtracting 16 from both sides, we have:
h^2 = 56.25
Now, to find the value of "h," we can take the square root of both sides:
√(h^2) = √56.25
h = √56.25
Calculating the square root of 56.25, we get:
h ≈ 7.5 ft
Therefore, the ladder reaches approximately 7.5 ft up the wall.