The sides of the triangle are 12 m, 16 m and 20 m respectively. Find its height from the top of the larger angle.

As we know, opposite the larger corner lies the larger side.

This means that the height will be drawn to the side, which is 20.

Let the length of the first segment obtained by dividing this side be equal to n.

Then the length of the second can be expressed in terms of 20 – n.

Both of them are legs in two rectangular triangles, then we express the height in each and write the equation:

12 ^ 2 – n ^ 2 = 16 ^ 2 – (20 – n) ^ 2;

144 – n ^ 2 = 256 – 400 + 40n – n ^ 2;

40n = 288;

n = 7.2.

Find the height:

√ (12 ^ 2 – 7.2 ^ 2) = √92.16 = 9.6.

Answer: Height = 9.6 cm.