Chapter 11, Problem 13GRFC

To determine

To calculate: The value of $h$ in the triangle.

Answer to Problem 13GRFC

The value of the $h$ in the triangle is $4.242\text{cm}$ .

Explanation of Solution

Given information: The triangle having side $3$ and $h$ and angle between these sides is ${45}^0$ .

Concept Used:

In the right angle triangle:

The value of the trigonometric function is

  $\cos \theta =\frac{\text{base}}{\text{hypotenuse}}$

Calculation:

In the given triangle the one angle of triangle is ${90}^0$

So, it is the right angle triangle.

For the angle ${45}^0$ the base of the triangle is $3$ and the hypotenuse is $h$ .

Then,

  $\begin{array}{l}\cos \theta =\frac{\text{base}}{\text{hypotenuse}}\\ \cos {45}^0=\frac{3}{h}\\ h=\frac{3}{\cos {45}^0}\\ h=\frac{3}{0.7071}\\ h=4.242\text{cm}\end{array}$

So, the value of the $h$ in the triangle is $4.242\text{cm}$ .

Conclusion:

The value of the $h$ in the triangle is $4.242\text{cm}$ .