Chapter 8, Problem 8CT

To determine

To find: the values of x and y

Answer to Problem 8CT

The value of x and y is $15,12$ respectively.

Explanation of Solution

Given Information: Two right triangles with a common side and measures of some of the sides being given in the figure.

Formula used:

The relationship between the legs of right triangle (shown in figure below) a , b and its hypotenuse c is obtained by Pythagoras theorem.

  

It can be expressed as,

  $\begin{array}{l}{c}^2=a^2+b^2\\ c=\sqrt{a^2+b^2}\end{array}$

Calculation: Consider the figure given below.

  

In ΔABC, $\angle C$ forms the right angle and the length of the altitude is denoted by the variable x. It can be calculated by Pythagoras theorem as,

  $\begin{array}{c}{17}^2=x^2+8^2\\ x=\sqrt{{17}^2-8^2}\\ =\sqrt{225}\\ =15\end{array}$

Similarly, the value of y can be calculated by Pythagoras theorem in ΔADC as,

  $\begin{array}{l}x=\sqrt{9^2+y^2}\\ y=\sqrt{x^2-9^2}\end{array}$

Substituting the value of x in the above equation, the value of y is obtained as follows.

  $\begin{array}{c}y=\sqrt{{15}^2-9^2}\\ =\sqrt{144}\\ =12\end{array}$