Question

Дви сторони трикутника доривнюють 8 см и 15 см,а кут миж ними 120.знайдить медиану,проведену до третьої сторони трикутника

Answer 1

за теоремою косинусів

с^2=a^2+b^2-2ab cos C

c^2=8^2+15^2-2*8*15*cos 120=409

медіана проведена до сторони с дорівнюэ

m(c)=1\2*корінь(2*(a^2+b^2)-c^2)

m(c)=1\2*корінь(2*(8^2+15^2)-(корінь(409))^2)=13\2=6.5 см

відповідь: 6.5 см

 

Answer 2

Triangle Median Calculation

To find the median drawn to the third side of the triangle, we can use the formula for calculating the length of a median in a triangle. The formula for the length of a median in a triangle is:

Length of Median = (1/2) * √(2 * (a^2 + b^2) - c^2)

Where: - a and b are the lengths of the two sides of the triangle that the median connects. - c is the length of the third side of the triangle.

In this case, the lengths of the two sides of the triangle are 8 cm and 15 cm, and the angle between them is 120 degrees.

Calculation

Using the given lengths of the sides and the angle between them, we can calculate the length of the median as follows:

Length of Median = (1/2) * √(2 * (8^2 + 15^2) - c^2)

Given that the angle between the sides is 120 degrees, we can use the law of cosines to find the length of the third side (c) of the triangle:

c^2 = a^2 + b^2 - 2ab * cos(C)

Where: - a and b are the lengths of the two sides of the triangle. - C is the angle between the sides.

Applying the Law of Cosines

Substituting the given values into the law of cosines:

c^2 = 8^2 + 15^2 - 2 * 8 * 15 * cos(120°)

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