# Triangles used in solving word problems

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1. Anne is pulling on a 60 foot rope attached to the top of a 48-foot tree while Walter is cutting the tree at its base. How far from the base of the tree is Anne standing. ( picture a triangle with the hypotenuse is 60 ft. and the back of the triangle is 48 ft from top to the base x ft. )

(the back is the right side and the hypotenuse is on the left)

2. Suppose at the kickoff of a football game , the receiver catches the football at the left side of the goal line and runs for a touchdown diagonally across the field . How many yards would he run ? ( A football field is 100 yards long and 160 feet wide.)

3. Betty observed that the lamppost in front of her house cast a shadow of length 8feet when the angle of inclination of the sun is 60 degrees . How tall is the lamppost? ( In a 30- 60- -90 right angle , the side opposite 30 is one half the length of the hypotenuse.) by the way the base is 8 t . (x ft is going down the back of the triangle )

(the back is on the left side and the hypotenuse is on the right)

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This solution provides examples of solving word problems based on triangles using diagrams.

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Please see the attached Word document for the solutions to these exercises.

All three of these problems use the Pythagorean formula:

In this formula is the length of the hypotenuse of a right triangle and and are the lengths of the two sides of the right triangle.

1. Anne is pulling on a 60 foot rope attached to the top of a 48-foot tree while Walter is cutting the tree at its base. How far from the base of the tree is Anne standing. ( picture a triangle with the hypotenuse is 60 ft. and the back of the triangle is 48 ft from top to the base x ft. ) (The back is the right side and the hypotenuse is on the left)

The description of the problem is shown in the diagram below. We are given the length of the hypotenuse and the ...

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