An object is 6m away from the base of a mast. The angle of depression of the object from the top pf the mast…

Analyze the question: An object is on the ground 6 m from the foot of a mast. From the top of the mast, the angle of depression to the object is 50°. We need the height of the mast.

Concept: The angle of depression from the top of the mast equals the angle of elevation from the object to the top (alternate angles). This gives a right-angled triangle where:

• the side opposite the 50° angle is the mast's height, h
• the side adjacent to the 50° angle is the 6 m distance

So we use the tangent ratio:

tan θ = opposite / adjacent

Solution:

tan 50° = h / 6

h = 6 × tan 50°

From tables or a calculator, tan 50° ≈ 1.1918

h = 6 × 1.1918 = 7.1508 ≈ 7.15 m

Answer: The height of the mast is 7.15 m, which is option C.

Check on the other options:

• A (8.60) would come from 6 / cos 50° ≈ 9.33, or other mistakes, and does not match anything correct.
• B (7.51) is a digit-swap trap of 7.15.
• D (1.19) is just tan 50° itself, which happens if you forget to multiply by 6.

Exam tip: Always draw a sketch and mark the angle of depression from the horizontal line at the top, not from the mast. Then remember SOH-CAH-TOA. Here you have the opposite and the adjacent sides, so use TOA (tan). Also memorize tan 50° ≈ 1.19 for quick checks, since it helps you eliminate wrong options fast.