Question

∠a is an acute angle in a right triangle. given that cosa=1213, what is the ratio for sina? enter your answer in the boxes as a fraction in simplest form.

Answer 1

`sina =(5)/(13)` is the answer.

Explanation:

It is given that in a right angle triangle angle B is a right angle triangle and
`cosa=(12)/(13)=(Base)/(hypotenuse)`

Now we see in the figure attached Base(adjacent side) is 12 and hypotenuse is 13.

We have to find sina.

since
`sina = (height)/(hypotenuse)`

We will find the length of hypotenuse with the help of Pythagoras theorem.

BC = √(13²-12²) = √(169-144) = √25 = 5

Now from the given triangle
`sina =(BC)/(AC)=(5)/(13)`

The correct option is
`sina =(5)/(13)`