A 12-foot ladder reaches 9 ft 6 in up a wall. How far up would a 20-foot ladder reach when placed at the same angle? Write the answer in feet with inches.
9.5/12 = x/20
x = 15.833 feet = 15 5/6 feet
= 15 feet 10 inches
A 20 foot extension ladder leaning against a building makes a 70.5 degrees angle with the ground. How far up the building does the ladder touch
To find out how far up a 20-foot ladder would reach when placed at the same angle, we can set up a proportion using the lengths of the two ladders.
First, let's convert the height reached by the 12-foot ladder to inches. We have 9 ft 6 in, which is the same as 9 ft + 6 in. Since 1 foot is equal to 12 inches, we can convert 9 ft to inches by multiplying 9 by 12, resulting in 108 inches. Adding 6 inches, we have a total of 114 inches reached by the 12-foot ladder.
Now, let's set up our proportion:
12 feet / 114 inches = 20 feet / x inches
Cross-multiplying the proportion, we have:
12 feet * x inches = 20 feet * 114 inches
Simplifying further, we get:
12x = 2280
Dividing both sides by 12, we find:
x = 190
Therefore, a 20-foot ladder will reach 190 inches up the wall. To convert this back to feet and inches, we divide 190 by 12 since there are 12 inches in a foot.
190 inches / 12 inches per foot = 15 feet remainder 10 inches.
So, a 20-foot ladder will reach 15 ft 10 in up the wall.