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WAEC Mathematics 2016 Paper

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Question : 28

Total: 49

In the diagram, TX is perpendicular to UW, |UX| = 1cm and |TX| = |WX| =

\sqrt{3}

cm. Find UTW

135^o
105^o
75^o
60^o

Solution:

Concept:

Use the tangent ratio in the two right triangles formed by the perpendicular line

TX

.

Explanation:

Since

TX \perp UW

, both

\triangle UTX

and

\triangle WTX

are right-angled at

X

.

Let

\alpha = \angle UTX

and

\beta = \angle XTW

.

Then

\angle UTW = \alpha + \beta

because

X

lies between

U

and

W

.

In

\triangle UTX

:

\tan \alpha = \frac{UX}{TX} = \frac{1}{\sqrt{3}}

.

So

\alpha = \tan^{-1}\left(\frac{1}{\sqrt{3}}\right) = 30^\circ

.

In

\triangle WTX

:

\tan \beta = \frac{WX}{TX} = \frac{\sqrt{3}}{\sqrt{3}} = 1

.

So

\beta = \tan^{-1}(1) = 45^\circ

.

Therefore,

\angle UTW = 30^\circ + 45^\circ = 75^\circ

.

Answer:

75^\circ

(Option C).

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