The three sides of a triangle are 4cm, 6cm and 8cm. (a) find the cosine of the largest angle
(b) show that the area of the triangle is 3√15cm²
(c) find the length of the shortest altitude of the triangle

In bold below.

Step-by-step explanation:

(a) The largest angle is opposite the largest side.

So by the Cosine Rule:

8^2 = 4^2 + 6^2 - 2*4*6 cos x

cos x =  (8^2 - 4^2 - 6^2) / (-2*4* 6)

= -0.25.

x = 104.48 degrees.

(b) Area of the triangle = 1/2 * 4 * 6 sin 104.48

= 11.62

= 3 √15.

(c)  The shortest altitude will have the longest sides as the base.

Area = 1/2 * altitude * base

3√15 = 1/2 * 8 * a

a = 3√15 / 4 cm

= 0.75√15 cm.