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)

2021-03-10
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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