Question

Trig/Geometry question.

Answer 1

The wrong thing keeps posting.

Answer 2

Finally!!

Answer 3

Do you know the value of \(\sin(45^{\circ})\)?

Answer 4

no

Answer 5

Hmm, do you know what sin is?

Answer 6

\[\sin45 = perpendicular / Hypotenous ... use this \]

Answer 7

opposite/hypotenuse

Answer 8

Exactly. The value for \(\sin(45^{\circ})\) is actually \(\dfrac{1}{\sqrt{2}}\).

Answer 9

But here, the "opposite" is 12 ft and the hypotenuse is length BC right?

Answer 10

Yes.

Answer 11

So we've got this equation:\[\sin(45) = \dfrac{12 ~ \rm ft}{BC}\]Since \(\sin(45) = 1/\sqrt 2\) we have\[\dfrac{1}{\sqrt{2}} = \dfrac{12}{BC}\]

Answer 12

Solve for \(BC\).

Answer 13

Would I just do it like a proportion?

Answer 14

Exactly.

Answer 15

\[\sqrt{2}\times12=8.48528137424\] \[BCtimes1=BC?\]

Answer 16

rounded to 8.5

Answer 17

\[BC = 12\times \sqrt{2} = 12\sqrt{2}\]

Answer 18

OK, that's the end of it. Thank you for walking me through it.

Answer 19

Yes, no problem!