Question

In triangle opq right angled at p op=7cm,oq-pq=1 determine the values of sinq and cosq

Answer 1

see explanation

Explanation:

let pq = x

given oq - pq = 1 then oq = 1 + x

Using Pythagoras' identity, then

(oq)² = 7² + x²

(1 + x)² = 49 + x² ( expand left side )

1 + 2x + x² = 49 + x² ( subtract 1 from both sides )

2x + x² = 48 + x² ( subtract x² from both sides )

2x = 48 ( divide both sides by 2 )

x = 24 ⇒ pq = 24

and oq = 1 + x = 1 + 24 = 25 ← hypotenuse

sinq =
`(opposite)/(hypotenuse)` =
`(7)/(25)`

cosq =
`(adjacent)/(hypotenuse)` =
`(24)/(25)`