Question

How to calculate $ \sin 37{}^\circ $ .

Answer 1

Hint: To solve this question we need to assume a right angled triangle $ \Delta ABC $ which is right angled at $ \angle B=90{}^\circ $ and sides having length $ AB=3 $ and $ BC=4\text{ units} $ . Then by using Pythagoras theorem we calculate the length of hypotenuse and by using the trigonometric ratio $ \sin \theta =\dfrac{\text{Perpendicular}}{\text{hypotenuse}} $ we find the value of $ \sin 37{}^\circ $ .

Complete step by step answer:
We have to calculate $ \sin 37{}^\circ $ .
Let us assume a right angle triangle $ \Delta ABC $ in which $ \angle B=90{}^\circ $ and $ AB=3 $ and $ BC=4\text{ units} $ .

Now, in right angle triangle $ \Delta ABC $ , by Pythagoras theorem we have
 $ A{{C}^{2}}=A{{B}^{2}}+B{{C}^{2}} $
By putting values, we get
 $ \begin{align}
  & \Rightarrow A{{C}^{2}}={{3}^{2}}+{{4}^{2}} \\
 & \Rightarrow A{{C}^{2}}=9+16 \\
 & \Rightarrow A{{C}^{2}}=25 \\
 & \Rightarrow AC=\sqrt{25} \\
 & \Rightarrow AC=5 \\
\end{align} $
Now, we know that $ \sin \theta =\dfrac{\text{Perpendicular}}{\text{hypotenuse}} $
So, we get $ \sin 37{}^\circ =\dfrac{3}{5} $ .
Note:
 As we assume a right triangle and $ \angle B=90{}^\circ $, then we know that $ 37{}^\circ $ is an acute angle so we can find the measure of an angle by using the triangle sum property. The Sum of all angles of a triangle must be equal to $ 180{}^\circ $. The accurate value of $ \sin 37{}^\circ $ is directly calculated by a scientific calculator also.