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WAEC Mathematics 2019 Paper

Question : 23

Total: 50

^{\circ}

^{\circ}

Solution:

Concept:

Use the tangent ratio in a right-angled triangle to find the unknown side.

Explanation:

\triangle XYZ

\angle XZY = 90^\circ

, so the triangle is right-angled at

Z

The side opposite the acute angle at

X

|YZ| = 32

cm.

The side adjacent to that same angle is

|XZ|

, which we need to find.

Thus,

\tan 52^\circ = \frac{|YZ|}{|XZ|} = \frac{32}{|XZ|}

Rearrange to get

|XZ| = \frac{32}{\tan 52^\circ}

Using

\tan 52^\circ \approx 1.2799

, we have

|XZ| \approx \frac{32}{1.2799} = 25.0

cm.

Correct to the nearest centimetre,

|XZ| = 25

cm.

Answer:

25

cm (Option B).

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