WAEC Mathematics 2025 Objective — Question 24

Question 24 of 51 from the West African Examinations Council (WAEC) Mathematics 2025 Objective paper, with the correct answer and a full explanation.

In the diagram, XYZ is an equilateral triangle of side 6 cm and T is the midpoint of XY. Find tan(angle XZT).

• A. 1/sqrt3Correct
• B. sqrt3/2
• C. sqrt3
• D. 1/2

Explanation

Using Pythagoras' theorem in the right triangle formed: ZT^2 = XZ^2 - XT^2 = 6^2 - 3^2 = 27, so ZT = sqrt27 = 3sqrt3. tan(XZT) = opposite/adjacent = XT/ZT = 3/(3sqrt3) = 1/sqrt3.

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