Find the values of the variables in each right triangle. 01510201141.png

Find the values of the variables in each right triangle. 01510201141.png

Question
Find the values of the variables in each right triangle.
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Answers (1)

2020-11-17
Apply Pythagoras theorem, to find the lengths of x and y.
Pythagoras Theorem states that in a right-angled triangle sum of squares of perpendicular adjacent sides of a triangle is equal to the square of the third side of the triangle.
In the smaller right-angled triangle:
\(\displaystyle{x}^{{2}}+{\left({3.6}\right)}^{{2}}={6}^{{2}}\)
\(\displaystyle{x}^{{2}}={36}-{12.96}\)
\(\displaystyle{x}^{{2}}={23.04}\)
\(\displaystyle{x}={4.8}\)
In the larger right-angled triangle:
\(\displaystyle{y}^{{2}}+{6}^{{2}}={\left({6.4}+{3.6}\right)}^{{2}}\)
\(\displaystyle{y}^{{2}}+{6}^{{2}}={10}^{{2}}\)
\(\displaystyle{y}^{{2}}={100}-{36}\)
\(\displaystyle{y}^{{2}}={64}\)
\(\displaystyle{y}={8}\)
Thus, the values of x and y are 4.8 and 8 respectively.
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