The angle of elevation of the top of a tree from a point 27m away and on the same horizontal ground as the…

Analyze the question: The tree stands vertically on level ground. You are 27 m from its foot, and the angle of elevation of its top is 30°. This forms a right-angled triangle:

• Adjacent side (ground distance) = 27 m
• Opposite side (tree height) = h
• Angle = 30°

Concept: When you know the adjacent and want the opposite, use tangent:

tan θ = opposite / adjacent

Solution:

tan 30° = h / 27

Since tan 30° = 1/√3:

h = 27 / √3

Rationalise by multiplying top and bottom by √3:

h = 27√3 / 3 = 9√3 m

Check against the options:

• A. 27 m: this would need a 45° angle, so it is wrong.
• B. 13.5√3 m ≈ 23.4 m: too large.
• C. 13.5√2 m: not related to 30°.
• D. 9√3 m ≈ 15.6 m: matches (27 × 0.5774 ≈ 15.59).

Tip: Memorise the tan values: tan 30° = 1/√3, tan 45° = 1, tan 60° = √3. With 30° and a distance that is a multiple of 3, the answer is usually a "something√3" after rationalising. Remember SOH-CAH-TOA: here the sides involved are Opposite and Adjacent, so use TOA.