Chapter 12.1, Problem 3CYU

To determine

Calculate the value of sinA.

Answer to Problem 3CYU

The value of $\sin A=\frac{\sqrt{33}}{7}$ .

Explanation of Solution

Given: It is given in the question that the value is $\cos A=\frac{4}{7}$ .

Concept Used:

In this, use the concept of pythagoras theorem and trigonometric ratios and the formula will be $h^2=p^2+b^2$ , $\sin \theta =\frac{p}{h},\cos \theta =\frac{b}{h},\tan \theta =\frac{p}{b},\csc \theta =\frac{h}{p},\sec \theta =\frac{h}{b},\cot \theta =\frac{b}{p}$ .

Calculation:

Here, use the trigonometric ratio formula:

  $CosA=\frac{4}{7}=\frac{b}{h}\Rightarrow b=4andh=7$

Now, use Pythagoras theorem where $b=4,h=7$ .

  $\begin{array}{l}{h}^2=p^2+b^2\\ 7^2=p^2+4^2\\ p^2=49-16\\ p^2=33\\ p=\sqrt{33}\end{array}$

Now, use the trigonometric ratios:

  $\sin A=\frac{\sqrt{33}}{7}$

Conclusion:

The value of $\sin A=\frac{\sqrt{33}}{7}$ .