A kite flies on a taut string of length 50m inclined at tan angle 54o to the horizontal ground. The height of the kite above the ground is

Analyze the question

The string is taut, so it forms a straight line from the ground to the kite. This makes a right-angled triangle:

• Hypotenuse = the string = 50 m
• Angle at the ground = 54°
• Opposite side to that angle = the height of the kite (h)

Concept

When you know the hypotenuse and want the side opposite an angle, use sine:

sin θ = opposite / hypotenuse

Solution

sin 54° = h / 50

h = 50 sin 54°

Check the other options:

• A: 50 tan 30° has no link to the 54° angle, so it is wrong.
• C: 50 tan 54° would treat 50 as the adjacent (horizontal) side, but 50 is the string (hypotenuse), so it is wrong.
• D: 50 sin 36° is wrong as written, because 36° is the angle at the kite (90° − 54°). The side opposite 36° is the horizontal distance, not the height. (The height would be 50 cos 36°, which equals 50 sin 54°.)

Answer: Option B, h = 50 sin 54° (about 40.45 m).

Tip: Use SOH-CAH-TOA. When the problem gives the hypotenuse and asks for the opposite side, go for SOH (Sine = Opposite/Hypotenuse). Also remember sin θ = cos(90° − θ), a common trap in WASSCE options.