The sides of a triangle are 14 cm, 48 cm and 50 cm. The perpendicular distance from the longest side to the midpoint of the shortest side is, in cm? (perpendicular to longest side)
+9466 
We want to find x .
First let's find cos a using the law of cosines: c2 = a2 + b2 - 2ab cos C
482 = 142 + 502 - 2(14)(50) cos a
2304 = 196 + 2500 - 1400 cos a
-392 = -1400 cos a
0.28 = cos a
And using the Pythagorean identity
0.282 + sin2 a = 1
sin2 a = 0.9216
sin a = 0.96
Now....let's just look at the little triangle.
sin a = opposite / hypotenuse
sin a = x / 7
0.96 = x / 7
7 * 0.96 = x
6.72 = x
+9466
We want to find x .
First let's find cos a using the law of cosines: c2 = a2 + b2 - 2ab cos C
482 = 142 + 502 - 2(14)(50) cos a
2304 = 196 + 2500 - 1400 cos a
-392 = -1400 cos a
0.28 = cos a
And using the Pythagorean identity
0.282 + sin2 a = 1
sin2 a = 0.9216
sin a = 0.96
Now....let's just look at the little triangle.
sin a = opposite / hypotenuse
sin a = x / 7
0.96 = x / 7
7 * 0.96 = x
6.72 = x
