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Sholpan [36]
2 years ago
8

Find the measure of the sides of angle ABC with vertices A(1,5), B(3,-2), and C(-3,0). Classify the triangle

Mathematics
1 answer:
Charra [1.4K]2 years ago
6 0

Answer:

AB=\sqrt{53},\ BC=\sqrt{40},\ CA=\sqrt{41}\\It\ is\ an\ acute\ triangle

Step-by-step explanation:

The distance between two points (x_1,y_1),\ (x_2,y_2) is given by \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}.

Here A(1,5),\ B(3,-2),\ C(-3,0) are the vertices of a triangle.

AB=\sqrt{(-2-5)^2+(3-1)^2}=\sqrt{(-7)^2+(2)^2}=\sqrt{49+4}=\sqrt{53}=7.28\ unit\\\\BC=\sqrt{(0+2)^2+(-3-3)^2}=\sqrt{(2)^2+(-6)^2}=\sqrt{4+36}=\sqrt{40}=6.32\ unit\\\\CA=\sqrt{(5-0)^2+(1+3)^2}=\sqrt{(5)^2+(4)^2}=\sqrt{25+16}=\sqrt{41}=6.40\ unit

Longest side=AB

AB^2=53\\BC^2+CA^2=40+41=81\\\Rightarrow AB^2

Hence this is an acute triangle.

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