Answer:
6(2 + √3)
Step-by-step explanation:
Given : Rectangle GHIJ inscribed in a circle. <em>GK⊥JH</em>, <em>GK</em> = 6 cm and <em>m∠GHJ</em>=15°.
To find: Radius<em>(KH)</em> =?
Sol: As given in figure 1, Since <em>GK⊥JH ∴ m∠GKH = 90° . Let GK = x cm.</em>
Now, In ΔGKH,
(∵<em> tan 15°</em> = 2 - √3)
On rationalizing the above expression,
Therefore, radius of the circle <em>(KH)</em> = 6 (2+√3)
This is how to find the value of <em>tan 15°</em>
<em>tan</em> 15° = <em>tan </em>(45° -30°)
Now using,
On rationalizing,
Taking 2 common from numerator,
<em>tan</em> 15° = 2 - √3
