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:
\[\begin{align}
  & \Rightarrow \dfrac{{{60}^{\circ }}}{{{90}^{\circ }}}=k \\
 & \Rightarrow k=\dfrac{2}{3} \\
\end{align}\]
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.