Item 22 refers to the following Diagram of a right angled triangle From the diagram above, sin C is (A) 5/13 (B)5/12 (C)12/13 (D)13/5

Question

asked Dec 9, 2024 217k views

1 Answer

Mike Petrov · Answer 1 · 2024-12-14T14:05:02+0000

Answer:

A)
(5)/(13)

Explanation:

Sine of any angle:
(opposte)/(hypotenuse)

To find the hypotenuse, we have to use pythagorean theorem:

a^(2) +b^(2) =c^(2)

$5^(2) +12^(2) =c^(2)\\ 25+144=c^(2) \\169=c^(2) \\√(169)=c\\ 13=c$

So, the hypotenuse is 13.

Now, the sine of angle C is the opposite side length, AB, over the hypotenuse, AC.

$(AB)/(AC)\\ =(5)/(13)$

So, A is the correct option. Hope this helps! :)