There is a sign that is 10ft on one side and 15ft on the other side (from the ground to the base of the sign), the billboard itself is 20ft.
The painter brings a 25ft ladder in length.
If the patch of ground 10ft from the base of the sign is used, at what point will the ladder touch the sign? Need two answers. 1st - length if measured from the ground and 2nd - if measured from the bottom of the sign.
The first sentence baffles me.
The first sentence is describing the shape and dimensions of the sign. It is saying that the sign is shaped like a rectangle, with one side measuring 10ft and the other side measuring 15ft, from the ground to the base of the sign.
Now, let's solve the problem.
To determine where the ladder will touch the sign, we need to use the Pythagorean theorem. The Pythagorean theorem states that in a right-angled triangle, the sum of the squares of the two shorter sides (legs) is equal to the square of the longest side (hypotenuse).
In this case, the ladder, ground, and the height of the sign form a right-angled triangle. The ladder acts as the hypotenuse, and the distance from the ground to the base of the sign is one of the legs.
First, let's calculate the length from the ground:
1. Using the Pythagorean theorem, we can find the height of the sign using the given measurements:
Height^2 + 10^2 = 25^2
Height^2 + 100 = 625
Height^2 = 525
Height ≈ 22.91 ft
2. So, if the ladder is measured from the ground, it will touch the sign at a height of approximately 22.91 feet.
Now, let's calculate the length from the bottom of the sign:
To find the length from the bottom of the sign, we need to subtract the height of the sign from the ladder's length.
3. Ladder length - Sign height
25 ft - 20 ft = 5 ft
So, if the ladder is measured from the bottom of the sign, it will touch the sign at a height of approximately 5 feet.
To summarize:
1. If measured from the ground, the ladder will touch the sign at a height of approximately 22.91 feet.
2. If measured from the bottom of the sign, the ladder will touch the sign at a height of approximately 5 feet.