Question

What is the value of csc A in the triangle below?
http://media.education2020.com/evresources/3111-13-05/mc004-1.jpg

Answer 1

1. Find the length of the hypotenuse, AC.
2. Find the sine of angle A.
3. Inverting this gives you csc A.

Answer 2

what would that be

Answer 3

I'd be very happy to guide you through the solution of this problem, but won't be giving out answers. Use the Pythagorean Theorem to find |AC|, then share your result with me.

Answer 4

ok

Answer 5

i got 18.35

Answer 6

All right. I'm not going to check that, but that result does look very reasonable.
Now that you have the hypotenuse, AC, how will you write sin A?

Hint: sin theta = opp side / hypotenuse.

Answer 7

i dont know how to do that

Answer 8

Haven't you encountered the sine and cosine functions yet?

If the hypotenuse is, as you say, 18.35, and the side opposite angle A is 16, then the sine of the angle A is \[\sin A=\frac{ 16 }{ 18.35 }\]

How much sense does this make to you?

Answer 9

Please look up the definitions of the sine and cosine and type them in here.

Answer 10

ok

Answer 11

the trigonometric function that is equal to the ratio of the side opposite a given angle (in a right triangle) to the hypotenuse.

Answer 12

cosine: he trigonometric function that is equal to the ratio of the side adjacent to an acute angle (in a right-angled triangle) to the hypotenuse.

Answer 13

Good. Please add these to a study/review sheet for later reference; you'll definitely need them.

\[\sin \theta = \frac{ opposite side }{ hypotenuse }\]

Here, \[\sin A = \frac{ 16 }{ 18.35 }\]

If you'll invert that, you'll have the csc of A.

"csc A" reads "the cosecant of the angle A" and is the reciprocal of sin A.

Try it: csc A = hyp / opp = reciprocal of sin A = ??