Question

I need help ASAP ! I don't understand it! Anyone??

Answer 1

I've shown two workings. One of them is to prove that the angles are complement to each other and the other to show that the answer is 7/5.

Answer 2

The answer is
`(7)/(5)`

Complimentary angles: the angles added up equal 90 degrees
When you have complimentary angles, the sine of one equals the cosine of the other and vice verse
Q and P are complimentary
sin(Q)=cos(P)
cos(Q)=sin(P)

Since you know that sin(Q)=
`(4)/(5)` , that also means that cos(P)=
`(4)/(5)`

Since sin(Q) is
`(leg)/(hypotenuse)` , you can use the Pythagorean Theorem to find the length of the last leg.

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

`a^(2) + (4)^(2) = (5)^(2)`

`a^(2) + 16 = 25`

`a^(2) = 9`

`a = 3`
(It's a 3,4,5 triangle)

Now you have the length of the other leg so cos(Q)=
`(3)/(5)`
cos(P)+cos(Q)
=
`(4)/(5) + (3)/(5)`
=
`(7)/(5)`

The answer is
`(7)/(5)`