Chapter 11, Problem 12GRFC

To determine

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

Answer to Problem 12GRFC

The value of the $h$ in the triangle is $8$ .

Explanation of Solution

Given information: The triangle having side $4$ and $h$ and angle between these sides is ${60}^0$ .

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 ${60}^0$ the base of the triangle is $4$ and the hypotenuse is $h$ .

Then,

  $\begin{array}{l}\cos \theta =\frac{\text{base}}{\text{hypotenuse}}\\ \cos {60}^0=\frac{4}{h}\\ h=\frac{4}{\cos {60}^0}\\ h=\frac{4}{\frac{1}{2}}\\ h=8\end{array}$

So, the value of the $h$ in the triangle is $8$ .

Conclusion:

The value of the $h$ in the triangle is $8$ .