A ladder leaning against a house makes an angle of 60° with the ground. The bottom of the ladder is 7 feet from the foundation of the house. What is the length of the ladder?
An image shows a right triangle. The legs of the triangle are formed by the side of a house and the ground. The hypotenuse of the triangle is formed by a ladder. The angle opposite the side of the house is labeled 60, with its adjacent side labeled 7 feet and the hypotenuse labeled x.
A.
6.06 feet
B.
12.12 feet
C.
14 feet
D.
42 feet
AAAaannndd the bot gets it wrong yet again!
cos(60°) = 7/x
I apologize for my mistake in the previous answer. As you have pointed out, the correct trigonometric function to use in this case is cosine, not sine. Here is the corrected solution:
cos(60°) = adjacent/hypotenuse
cos(60°) = 7/x
x = 7/cos(60°)
x = 14 feet
Therefore, the correct answer is C. 14 feet.
Can you help with math too?
Yes, I'm happy to help you with math! What do you need help with?
I am having trouble subtracting numbers without a calculator.
Sure, I can help you with that! Do you have any specific problems you need help with, or would you like a general explanation of the subtraction process?
Give me an explanation
Sure! When subtracting two numbers, the first step is to align the numbers vertically, with the digits in the same place values lined up with each other. Then, starting from the rightmost digit, subtract the top number from the bottom number in each place value column.
If the top number is larger than the bottom number in a column, simply write the difference in that place value column. However, if the bottom number is larger than the top number in a column, you will need to "borrow" from the place value to the left. To do this, subtract 1 from the place value to the left and add 10 to the current place value. Then, proceed with subtracting the numbers in that column as usual.
Continue these steps for each place value column, carrying any "borrowed" amounts as necessary, until all columns have been subtracted. The final result is the difference between the two original numbers.
Here's an example to illustrate:
527
- 341
-------
186
In the ones place, 7 - 1 = 6. In the tens place, 2 - 4 = -2, but this requires borrowing from the hundreds place. So, we add 10 to 2 and get 12, then subtract 4, which gives us 8. Then, we subtract 3 - 1 = 2 in the hundreds place.
Therefore, the final answer is 186.
Cool can you help with specific problem?
Sure, I can help with a specific problem. What problem do you have in mind?
What is 300-299 ?
300 - 299 = 1.
So the difference between 300 and 299 is 1.
What is 300-310 ?
300 - 310 = -10.
So the difference between 300 and 310 is -10.
Why is it negative?
The difference of 300 - 310 is negative because we are subtracting a larger number (310) from a smaller number (300), which means that we will end up with a negative result.
When we subtract a larger number from a smaller number, the result will always be negative, unless we are subtracting two identical numbers (which would give 0 as the result). In this case, since 310 is ten more than 300, the result is -10.
Using trigonometry, we can use the sine function to find the length of the ladder:
sin(60°) = opposite/hypotenuse
sin(60°) = 7/x
x = 7/sin(60°)
x = 8.08 feet (rounded to the nearest hundredth)
Therefore, the length of the ladder is approximately 8.08 feet, which is closest to answer choice A. 6.06 feet.