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Lines, Triangles and Circles · Question 34 of 67

Question 34

MediumOriginal question

At a certain moment Harleen, who is 1.8 m tall, casts a shadow 2.4 m long. At the same moment a water tower casts a shadow 36 m long. How tall is the tower?

Options for question 34

Show the answer and explanation
CorrectNot quiteAnswer A

Correct answer: A

Explanation

  1. Harleen and her shadow, and the tower and its shadow, form similar right triangles (the sun's rays make the same angle).

  2. Height ÷ shadow is the same: h36=1.82.4=34\frac{h}{36} = \frac{1.8}{2.4} = \frac{3}{4}.

  3. h=36×34=27h = 36 \times \frac{3}{4} = 27 m.

Worth noting

48 m comes from flipping the ratio (shadow ÷ height). A quick check: her shadow is longer than she is, so the tower must be shorter than its 36 m shadow.

Concept
Similar triangles from shadows
Typical time
70 s
Your time
—
The rule this testsSimilarity and Pythagoras
Practise this chapter →

Ten questions from Lines, Triangles and Circles, at your own pace.

Practise this chapter →

Ten questions from Lines, Triangles and Circles, at your own pace.