Question

∠A is an acute angle in a right triangle. Given that cos A=12/13, what is the ratio for sin A? Enter your answer in the boxes as a fraction in simplest form

Answer 1

5/13. Very sure on this one!

Answer 2

sin A =
`(5)/(13)`

Explanation:

As per the statement:

∠A is an acute angle in a right triangle.

Given that:

`\cos A = (12)/(13)`

We have to find Sin A:

Using the formula:

`\sin A= √(1-\cos^2 A)`

Substitute the given values we have;

`\sin A= \sqrt{1-((12)/(13))^2}`

⇒
`\sin A = \sqrt{1-(144)/(169)} = \sqrt{(169-144)/(169)}`

⇒
`\sin A = \sqrt{(25)/(169)} = \sqrt{(5^2)/(13^2)} = (5)/(13)`

Therefore, the value of sin A as a fraction in simplest form is,
`(5)/(13)`