Given that x = 5/13 and y = 8/17, where x and y are acute, find (x+y).

Correct Answer is : 140221140/221221140

Correct Answer is : 140221140/221221140

Test Index

WAEC Further Mathematics 2017 Paper

Question : 18

Total: 40

Given that

\sin x = \frac{5}{13}

\sin y = \frac{8}{17}

\cos(x+y)

Solution:

Concept:

Use the compound angle formula:

\cos(x+y)=\cos x\cos y-\sin x\sin y

Explanation:

Since

x

and

y

are acute, all trigonometric ratios are positive.

For angle

x

: opposite

=5

, hypotenuse

=13

Adjacent side

=\sqrt{13^2-5^2}=\sqrt{144}=12

So,

\cos x=\frac{12}{13}

For angle

y

: opposite

=8

, hypotenuse

=17

Adjacent side

=\sqrt{17^2-8^2}=\sqrt{225}=15

So,

\cos y=\frac{15}{17}

Now substitute into the formula:

\cos(x+y)=\left(\frac{12}{13}\right)\left(\frac{15}{17}\right)-\left(\frac{5}{13}\right)\left(\frac{8}{17}\right)

=\frac{180}{221}-\frac{40}{221}=\frac{140}{221}

Answer:

\frac{140}{221}

, which is option B.

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