Solve for the unknown.*

13.14

Step-by-step explanation:

sin 37.5 deg = 8/x

x = 8/sin 37.5 deg

x = 13.14

(I was thinking about it as a right angled triangle although the qn did not specify but idt you can solve it by using sine / cosine rule so TOA CAH SOH may be the only one and the most direct method to solve it)

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