Chapter SH, Problem 10.4.7EP

To determine

Missing measure of a triangle.

Answer to Problem 10.4.7EP

The missing measure is $b=8.5cm$ .

Explanation of Solution

Given:

For a triangle,

Two sides are given:

  $\begin{array}{l}a=3cm\\ c=9cm\end{array}$

Where,

  $c$ is the hypotenuse and to find missing measure which is. $b$

Concept Used:

The Pythagoras theorem of right angled triangle is used.

When two sides of triangle are given and the remaining one side is to be found, Pythagoras theorem is used.

It is given as $c^2=a^2+b^2$

  $a,b$ are the sides of right angled triangle and $c$ is the hypotenuse.

Calculation:

For a triangle,

Consider the sides of triangle as $a,b,c$ and $c$ is the hypotenuse side given.

Now Using Pythagoras Theorem to find the missing measure $b$

  $c^2=a^2+b^2$

Substitute the values in the above formula,

  $c^2=a^2+b^2$

Where,

  $\begin{array}{l}a=3cm\\ c=9cm\end{array}$

  $\begin{array}{l}{9}^2=3^2+b^2\\ 81=9+b^2\end{array}$

Now subtracting $9$ from $81$ to find $b^2$

  $\begin{array}{l}81-9=b^2\\ 72=b^2\end{array}$

Taking square root on both the sides

  $\begin{array}{l}\sqrt{72}=b\\ b=8.48cm\approx 8.5cm\end{array}$

Conclusion:

Hence, the missing measure is $b=8.5cm$ .