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Given that sinx=513 and \(\sin y = \frac{8}...

Given that sinx=513 and siny=817, where x and y are acute, find cos(x+y).

A.

130221

B.

140221

C.

140204

D.

22023

Correct answer is B

cos(x+y)=cosxcosysinxsiny

Given sin of an angle implies we have the value of the opposite and hypotenuse of the right-angled triangle. We find the adjacent side using Pythagoras' theorem.

Adj2=Hyp2Opp2

For triangle with angle x, adj=13252=144=12

For triangle with angle y, adj=17282=225=15

\cos(x+y) = (\frac{12}{13}\times\frac{15}{17}) - (\frac{5}{13}\times\frac{8}{17}) = \frac{180}{221} - \frac{40}{221}

= \frac{140}{221}