Question

Paisley set up the following equation to solve a math problem: 33 +57 + x = 180. What could the x represent? A. The third angle in a triangle where the other two angles measure 33° and 57° the hypotenuse of a right triangle with the legs of lengths 33 units and 57 units C. The score needed by a bowler to obtain an average of 180, when his previous two scores were 33 and 57 the third side of a triangle with an area of 180 square units, where the other sides are 33 units and 57 units

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Answer 1

A. The third angle in a triangle where the other two angles measure 33° and 57°

Explanation:

You want to know the sort of math problem that might be solved using the equation ...

• 33 +57 +x = 180

A. Triangle

You know the sum of angles in a triangle is 180°, so if two of them are 33° and 57°, the unknown angle x in a triangle can be found using Paisley's equation.

B. Hypotenuse

If Paisley is trying to find the hypotenuse of a right triangle with legs 33 and 57, we expect to see the equation ...

33² +57² = x²

C. Bowling

The average is obtained by dividing the total of scores by the number of scores. The score required for an average of 180 could be found using the equation ...

(33 +57 +x)/3 = 180

This is not Paisley's equation.

D. Third side

The area of a triangle is related to the side lengths by Heron's formula. It can also be found using a couple of trig formulas. In either event, the relation is very much different from the one Paisley wrote.

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Additional comment

Paisley's equation gives x=90, indicating her triangle is a right triangle.

If 33 and 57 are side lengths of a triangle with an area of 180 square units, the third side is about 25.40752 units long. This value is not obtained using Paisley's equation.

For an average of 180, the bowling score would need to be 450, a score that is not possible in one game.

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