The angle of elevation of the top T of a pole from a point X on the horizontal ground is 32°, if X is 68 m…

Analyze the question: The pole stands vertically on level ground. From X, 68 m from the foot F, the angle of elevation to the top T is 32°. This gives a right-angled triangle XFT with the right angle at F.

• Adjacent side (XF) = 68 m
• Opposite side (FT) = the height we want
• Angle at X = 32°

Concept: Since we have the opposite and adjacent sides, we use the tangent ratio:

tan θ = opposite / adjacent

Solution:

tan 32° = FT / 68

FT = 68 × tan 32°

From tables or a calculator, tan 32° ≈ 0.6249

FT = 68 × 0.6249 ≈ 42.49 ≈ 42.5 m

Answer: The height of the pole is 42.5 m, which is option E.

Tip: Remember SOH-CAH-TOA. When the question gives the adjacent side and asks for the opposite (or the reverse), use TOA, the tangent ratio. A quick sense check: for angles under 45°, tan is less than 1, so the height must be less than the horizontal distance (here, less than 68 m). That immediately rules out A and B.