Question

Express in terms of a right angle, the angle ${{60}^{\circ }}$.

Answer 1

Hint: We know that the right angle is an angle whose measure is equal to ${{90}^{\circ }}$. For the above equation we suppose that given angle in the question is equal to k times of a right angle i.e. ${{90}^{\circ }}$ then equating them, we will find the value of k.

Complete step-by-step answer:
We have been given the angle ${{60}^{\circ }}$ which we have to express in terms of a right angle.
Let us suppose ${{60}^{\circ }}$ is equal to k times a right angle $\left( {{90}^{\circ }} \right)$.
$\Rightarrow {{60}^{\circ }}=k\times {{90}^{\circ }}$
On dividing the whole equation by ${{90}^{\circ }}$ on both the sides of the equation, we get as follows:

& \Rightarrow \dfrac{{{60}^{\circ }}}{{{90}^{\circ }}}=k \\\ & \Rightarrow k=\dfrac{2}{3} \\\ \end{aligned}$$ Therefore, the angle $${{60}^{\circ }}$$ can be expressed in the form of right angle as $$\dfrac{2}{3}$$ times of a right angle i.e. $${{90}^{\circ }}$$. Note: In this type of questions, first of all check that the given angle is completely in degree or radians. Then suppose the angle to be equal to k times the right angle and the unit of the measurement must be the same. If the given angle is in degrees, then we will take right angle equal to $${{90}^{\circ }}$$ and if the given angle is in radian then you will take right angle equal to $$\dfrac{\pi }{2}$$ radians. Also, sometimes in order to calculate the value of ‘k’ we just divide $${{90}^{\circ }}$$ by the given angle by mistake. So be careful while calculating the value of k.