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

Question
Find the values of the variables in each right triangle.

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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