4 years ago

If m3=40, what is m2

Mathematics

1 answer:

polet [3.4K]4 years ago

8 0

Answer:

m<2 = 50°

Step-by-step explanation:

Right triangle

m<3 = 40

so m<2 = 90 - m<3

m<2 = 90 - 40

m<2 = 50

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

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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