Multiple choice

The distance between the two trees of height 961 cm and 841 cm is ‘y’ meters. If two angles of elevation of their respective top from the bottom of the other are complementary to each other then the value of ‘y’ in cm is :

  1. 6.77 cm

  2. 7.88 cm

  3. 8.99 cm

  4. 10.11 cm
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

When angles of elevation are complementary, if α + β = 90°, then tanα × tanβ = 1. This gives h1/y × h2/y = 1, so y² = h1 × h2 = 961 × 841 = 808801. Therefore y = √808801 = 899 cm = 8.99 m. This elegant property emerges from tan(90-α) = cotα = 1/tanα.

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