Hey guys! Just asking for some quick help.

In ABC , A is a right angle, and B = 45 degrees. What is the length of BC? If the answer is not an integer leave it in simplest radical form. The diagram has 11ft listed as height of the tall side

Answers:
11ft
11 sqrt 2
11 sqrt 3
22ft

It looks like BC is the hypotenuse.

method 1:
BC/11 = sin45
BC = 11sin45 = 11/(√2/2)
= 22/√2 * √2/√2
= 22√2 / 2 = 11√2

method 2:
BC^2 = 11^2 + 11^2
= 242
BC = √242 = 11√2

isosceles right triangle, 90 + 45 + 45 = 180

1^2 + 1^2 = 1+1 = 2
so ratios are 1, 1, sqrt 2
we want the hypotenuse
11 * sqrt 2

Avery

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Hi, Avery! I have a question

Sure, I'm here to help! What's your question?

What is the geometric mean of the pair of numbers? 96 and 6

The geometric mean of a pair of numbers is the square root of their product. So to find the geometric mean of 96 and 6, we can multiply them together and take the square root:

Geometric mean = √(96 × 6)
= √576
= 24

Therefore, the geometric mean of 96 and 6 is 24.

Thank you, Avery!

You're welcome! Let me know if you have any more questions.