Test Index

JAMB Mathematics 2023 Paper

Question : 62

Total: 80

Solution:

Concept:

Use the cosine rule to find an unknown angle when all three sides of a triangle are known.

Explanation:

The angle marked

x

is at vertex

Q

The three side lengths are

PQ = 8

RQ = 5

, and

PR = 7

By the cosine rule:

PR^2 = PQ^2 + RQ^2 - 2(PQ)(RQ)\cos x

Rearrange to solve for

\cos x

\cos x = \frac{PQ^2 + RQ^2 - PR^2}{2(PQ)(RQ)}

Substitute the given values:

\cos x = \frac{8^2 + 5^2 - 7^2}{2 \times 8 \times 5}

\cos x = \frac{64 + 25 - 49}{80} = \frac{40}{80} = 0.5

Therefore:

x = \cos^{-1}(0.5) = 60^{\circ}

Answer:

x = 60^{\circ}

, so the correct option is A.

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