Question

mixed practice! find the value of
10.
28
45°
x =
y =

Explanation:

Step1: Identify the triangle type

This is a right - angled isosceles triangle (since one angle is \(90^{\circ}\) and another is \(45^{\circ}\), so the third angle is also \(45^{\circ}\), making it an isosceles right - triangle). In an isosceles right - triangle, the legs are equal, so \(x = y\).

Step2: Apply the Pythagorean theorem

By the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\). Here \(a = x\), \(b = y\) (and \(x = y\)), \(c = 28\). Substituting \(y=x\) into \(x^{2}+y^{2}=28^{2}\), we get \(x^{2}+x^{2}=784\).

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Since \(y = x\), \(y=14\sqrt{2}\)

Answer:

\(x = 14\sqrt{2}\), \(y = 14\sqrt{2}\)