Given the triangle XYZ above, calculate the value of Cot \(\theta\) and the length XY, respectively
Attached Figure / Diagram
A
\(\frac{\sqrt{48}}{13}\), \(\sqrt{48}\)
B
\(\frac{\sqrt{48}}{11}\), \(\sqrt{48}\)
C
\(\frac{\sqrt{13}}{11}\), \(\sqrt{13}\)
D
\(\frac{13}{\sqrt{48}}\), \(\sqrt{48}\)
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
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 = \(\frac{\text{adjacent}}{\text{opposite}}\) = \(\frac{\text{XY}}{\text{YZ}}\) = \(\frac{\sqrt{48}}{11}\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #74203)