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If tan x° = 52\dfrac{5}{2}, the length of CB is :

  1. 0.4 m

  2. 40 m

  3. 50 m

  4. 80 m

If tan x° = 5/2, the length of CB is : Heights and Distances, Concise Mathematics Solutions ICSE Class 10.

Heights & Distances

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Answer

We know that,

tan θ = PerpendicularBase\dfrac{\text{Perpendicular}}{\text{Base}}

From figure,

In △ ABC,

⇒ tan x° = ABCB\dfrac{AB}{CB}

⇒ 52=100CB\dfrac{5}{2} = \dfrac{100}{CB}

⇒ CB = 2×1005=2005\dfrac{2 \times 100}{5} = \dfrac{200}{5} = 40 m.

Hence, Option 2 is the correct option.

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