Chapter 13.1, Problem 20PPS

To determine

Calculate the value of tanB .

Answer to Problem 20PPS

The value is $\tan B=\frac{4}{2\sqrt{5}}$ .

Explanation of Solution

Given: It is given in the question that the value of $\sin B=\frac{4}{9}$ .

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:

  $\sin B=\frac{4}{9}=\frac{p}{h}\Rightarrow p=4andh=9$

Now, use Pythagoras theorem where $p=4andh=9$ .

  $\begin{array}{l}{h}^2=p^2+b^2\\ 9^2=4^2+b^2\\ b^2=36-16\\ b^2=20\\ b=\sqrt{20}=2\sqrt{5}\end{array}$

Now, use the trigonometric ratios:

  $\tan B=\frac{4}{2\sqrt{5}}$

Conclusion:

The value is $\tan B=\frac{4}{2\sqrt{5}}$ .