Question
Question: Express in terms of a right angle, the angle \[{{130}^{\circ }}30'\]....
Express in terms of a right angle, the angle 130∘30′.
Solution
Hint: We know that a right angle is equal to 90∘. We will first convert the given angle in degrees completely for which we will use the following conversion:
1′=(601)∘
Complete step-by-step answer:
After converting the given angle completely into degrees, we will suppose the given angle is equal to ‘k’ times the right angle and thus equating them we will find the value of ‘k’.
We have been given the angle 130∘30′ which we have to express in terms of right angle.
We know that 1′=(601)∘
⇒30′=(30×601)∘=(21)∘
⇒130∘30′=130∘+30′
Substituting the value of 30’ in degrees, we get as follows:
⇒130∘30′=130∘+0.5∘=130.5∘
Let us suppose 130.5∘ is equal to k times a right angle.
⇒130.5∘=k×90∘
On dividing the above equation by 90∘, we get as follows: