Given the triangle XYZ above, calculate the value of Cot \(\theta\) and the length XY, respectively

Assessment: JAMB UTME - Mathematics - 2025 Subject: General Mathematics

Question 1 Report

\(\frac{\sqrt{48}}{13}\), \(\sqrt{48}\)

\(\frac{\sqrt{48}}{11}\), \(\sqrt{48}\)

\(\frac{\sqrt{13}}{11}\), \(\sqrt{13}\)

\(\frac{13}{\sqrt{48}}\), \(\sqrt{48}\)

Answer Details

The triangle XYZ is a right-angled triangle at Y, with opposite side to θ (YZ) = 11 cm and hypotenuse (XZ) = 13 cm.

The length of XY = \(\sqrt{(13^2 - 11^2)}\) = \(\sqrt{(169 - 121)}\) = \(\sqrt{48}\) cm (or 4\(\sqrt{3}\) cm in simplified form).

Cot θ = \(\frac{\text{adjacent}}{\text{opposite}}\) = \(\frac{\text{XY}}{\text{YZ}}\) = \(\frac{\sqrt{48}}{11}\)

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