The picture shows a triangular island: A right triangle is shown with an acute angle equal to 55 degrees. The length of the side of the triangle opposite to the acute angle is r. The length of the side of the triangle adjacent to the acute angle is s. The length of the hypotenuse is q.

Which expression shows the value of q?

r cos 55°
r sin 55°
s over sin 55 degrees
s over cos 55 degrees

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4

the linear relationship that represents a variation in direct proportion is the linear function that varies according to the numbers of its domain, for example the cost of producing x number of items can be represented in direct proportion by f (x) = mx + b, where m is the constant of proportionality, x the number of articles produced and b the fixed cost

use photo math thats what i use u can scan the problem and it tells u the answer