Question

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

Answer 1

The answer is $\frac{7}{5}$

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)=$\frac{4}{5}$ , that also means that cos(P)=$\frac{4}{5}$

Since sin(Q) is $\frac{leg}{hypotenuse}$ , 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)=$\frac{3}{5}$
cos(P)+cos(Q)
=$\frac{4}{5} + \frac{3}{5}$
=$\frac{7}{5}$

The answer is $\frac{7}{5}$

Answer 2

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.