Answered: A Right Triangular field has a length…

Algebra: Structure And Method, Book 1

(REV)00th Edition

ISBN:9780395977224

Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Chapter11: Rational And Irrational Numbers

Section: Chapter Questions

Problem 12CT

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Question

A Right Triangular field has a length of 110 ft and the hypotenuse 220 ft. a) Find the third side of the field and Find the area of the field in square feet.

Expert Solution

Step 1

consider the right triangular field as shown

the third side can be calculated using the Pythagoras theorem

$\begin{array}{rcl} A C^{2} & = & B C^{2} + A B^{2} \\ 220^{2} & = & 110^{2} + A B^{2} \\ 48400 & = & 12100 + A B^{2} \\ 48400 - 12100 & = & A B^{2} \\ 36300 & = & A B^{2} \\ A B & = & \sqrt{36300} \\ A B & = & 110 \sqrt{3} \end{array}$

The third side of the triangle is $110 \sqrt{3}$ ft.

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