A man is 40m from the foot of a cliff of height 23m. Calculate the angle of elevation of the top of the cliff from the man

Analyze the question: The man stands 40 m from the foot of the cliff (the adjacent side), and the cliff is 23 m high (the opposite side). We need the angle of elevation θ.

Concept: For a right-angled triangle, tan θ = opposite / adjacent (SOH-CAH-TOA).

Solution:

tan θ = 23 / 40 = 0.575

θ = tan⁻¹(0.575)

Checking nearby values:

• tan 30° = 0.5774, which is slightly above 0.575
• tan 29.9° ≈ 0.5750

So θ ≈ 29.9°.

Converting to degrees and minutes: 0.9° × 60 = 54′, so θ ≈ 29° 54′.

Checking the options:

• A (50° 54′): too large
• B (35° 06′): too large
• C (30° 00′): tan 30° = 0.5774, which is close but not exact
• D ("290 90′"): this is a misprint and not a valid angle
• E (29° 54′): matches our result

Answer: E. 29° 54′

Tip: In elevation questions, draw a quick right-angled triangle and label the sides. Height is opposite and distance on the ground is adjacent, so use tan. When two options are close (like 30° 00′ and 29° 54′), compute precisely on your calculator rather than rounding.