Question

Can someone help me solve this probelm? (ignore the numbers typed in)

Answer 1

see explanation

Explanation:

given

cosΘ =
`(8)/(17)` =
`(adjacent)/(hypotenuse)`

to find the third side ( opposite side of the right triangle )

use Pythagoras' identity

opp² + 8² = 17²

opp² + 64 = 289 ( subtract 64 from both sides )

opp² = 225 ( take square root of both sides )

opp =
`√(225)` = 15

then given sinΘ < 0

sinΘ =
`(opposite)/(hypotenuse)` = -
`(15)/(17)`

secΘ =
`(1)/(cos0)` =
`(1)/((8)/(17) )` =
`(17)/(8)`

tanΘ =
`(sin0)/(cos0)`

=
`(-(15)/(17) )/((8)/(17) )`

= -
`(15)/(17)` ×
`(17)/(8)` = -
`(15)/(8)`