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JAMB Mathematics 2011 Paper

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Question : 30

Total: 46

In a right angled triangle, if tan

\theta

\frac{3}{4}

\theta

\theta

?

$\frac{2}{3}$
$\frac{3}{5}$
$\frac{1}{5}$
$\frac{4}{5}$

Solution:

Concept:

Use the sides of a right triangle from

\tan \theta = \frac{3}{4}

to find

\sin \theta

and

\cos \theta

.

Explanation:

In a right triangle,

\tan \theta = \frac{\text{opposite}}{\text{adjacent}} = \frac{3}{4}

.

So the two shorter sides are

3

and

4

.

Using Pythagoras, the hypotenuse is

\sqrt{3^2 + 4^2} = \sqrt{25} = 5

.

Therefore,

\sin \theta = \frac{3}{5}

and

\cos \theta = \frac{4}{5}

.

Now compute:

\cos \theta - \sin \theta = \frac{4}{5} - \frac{3}{5} = \frac{1}{5}

.

Answer:

\frac{1}{5}

(Option C).

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