Question

How do you solve $\sin 45 = \dfrac{{12}}{x}?$

Answer 1

Hint:As we know that the above question is of trigonometric functions as sine is trigonometric ratio and it considered as one of the most important trigonometric ratios as it is used to find out the unknown values of angles and length of the sides of the right angled triangle. The sine formula in the right angled triangle is $\sin \theta = \dfrac{p}{h}$ where $p$ is the perpendicular and $h$ is the hypotenuse. There are two most important trigonometric functions that are used widely are Sine and Cosine.

Complete step by step solution:
In the above question we have $\sin 45 = \dfrac{{12}}{x}$. As we know that the exact value of $ \sin 45$ is $\dfrac{1}{{\sqrt 2 }}$.
Now by substituting the value of sine degree and solving the equation: $\dfrac{1}{{\sqrt 2 }} =\dfrac{{12}}{x}$, by doing cross multiplication we get $12 \times \sqrt 2 = x$. It gives us $x =12\sqrt 2 $.
Hence the required value of $x$ is $12\sqrt 2 $.

Note: Before solving this type of question we should have the complete knowledge of trigonometric ratios and their values and how to derive it. It is necessary to know the values as we cannot find the value of any variable without knowing their values. We should also know that the values of sine function can be either positive or negative, these values are dependent on the quadrants in which they lie. If the particular sine values which we want to now lie in the positive quadrant i.e. in the first and third quadrant, then the value will also be positive. But if it lies in the negative quadrant then the value will also be negative.