Question

A is an acute angle in a right triangle, Given that Sin A= 7/25, what is the ratio for Cos A? Enter your answer in the box as a fraction in simplest form.

Answer 1

`\sin \theta = (opp)/(hyp)`


`\sin A = (7)/(25) = (opp)/(hyp)`


`a^2 + b^2 = c^2`


`a^2 + 7^2 = 25^2`


`a^2 = 625 - 49`


`a = √(576)`


`a = 24`


`adj = a = 24`


`\cos A = (adj)/(hyp)`


`\cos A = (24)/(25)`

Answer 2

Find the adjacent side of the triangle ...
7² + x² = 25²
x² = 25² - 7²
x² = 576
x = 24
The adjacent side of the triangle is 24

Given that sin A =
`(7)/(25)`
Since sin A =
`(o)/(h)`
We can conclude that o = 7 and h = 25

cos A =
`(a)/(h)`
cos A =
`(24)/(25)`