A right-angled triangle ABC is given. It is known that: a ^ 2-b ^ 2 = 28, c = 10. We need to find a.
| August 6, 2021 | education
By condition, BC ^ 2 – AC ^ 2 = 28 cm. (1)
By the Pythagorean theorem, AB ^ 2 = AC ^ 2 + BC ^ 2 (2).
Let us solve the system of two equations by the substitution method.
AC ^ 2 = BC ^ 2 – 28.
AB ^ 2 = BC ^ 2 – 28 + BC ^ 2.
100 = 2 * BC ^ 2 – 28.
2 * BC ^ 2 = 128.
BC ^ 2 = 64.
BC = a = 8 cm.
Answer: The length of side a is 8 cm.
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