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AP EAMCET · Maths · Properties of Triangles

The base of a triangle is 80 and one of the base angles is \(60^{\circ}\). If the sum of the lengths of the other two sides is 90, then the shortest side is of length

  1. A \(15\)
  2. B \(21\)
  3. C \(19\)
  4. D \(17\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(17\)

Step-by-step Solution

Detailed explanation

Let the sides be \(a\), \(b\), and \(c\). Given \(c=80\) and \(\angle A = 60^{\circ}\). Given \(a+b=90 \Rightarrow a=90-b\). \(a^2 = b^2 + c^2 - 2bc \cos A\) \((90-b)^2 = b^2 + 80^2 - 2 \cdot b \cdot 80 \cdot \cos 60^{\circ}\)…