# How to find the height of the triangle knowing 3 of it 9 10 17.

June 28, 2021 | education

| Dano: Triangle ABC;

AC = B = 9;

Bc = a = 10;

AB = C = 17.

Find: BN height -?

Decision:

1) We find S ABC = √R (R – A) (P – B) (P – C) according to the Geron formula. Where p is a half-meter. Then p = (a + B + C) / 2 = (9 + 10 + 17) / 2 = 36/2 = 18. Consequently, A ABC = √18 (18 – 10) (18 – 9) (18 – 17) = √18 * 8 * 9 * 1 = √1 296 = 36;

2) Another area of the triangle can be found according to the formula S AUC = 1/2 * BН * AC = 1/2 * BН * B;

36 = 1/2 * BН * 9;

BН = 36: 9: 1/2;

BН= 4 * 2

BН = 8 – height spent on the AC side.

Answer: The height is 8.

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