Trigonometry & Inverse Trigonometry
Circumradius of Triangle
Grade 11
Question:
<p>In a triangle with one angle <strong>π/3</strong>, the lengths of the sides form an A.P. If the length of the greatest side is 7 cm, the radius of the circumcircle of the triangle is</p>
<p>(a) <strong>7√3/3</strong> cm</p>
<p>(b) <strong>7√3/3</strong> cm</p>
<p>(c) <strong>7√3/3</strong> cm</p>
<p>(d) <strong>7√3/3</strong> cm</p>
Step-by-Step Solution
Key Concept: Use the constraint that sides are in A.P. combined with the law of cosines to find the circumradius using \(R = \frac{a}{2\sin A}\).
<p>Given: One angle is \(\frac{\pi}{3}\), sides in A.P., greatest side = 7 cm.</p><p>Let sides be \(a-d, a, a+d\) where \(a+d = 7\) (greatest side).</p><p>The angle \(\frac{\pi}{3}\) is opposite to one of these sides. Using the law of cosines and properties of A.P., we can determine that \(R = \frac{7\sqrt{3}}{3}\) cm.</p>
Correct Answer: A