Explanation:
Before we proceed, we must understand that we are dealing with a system of right angled triangles.
There are two types of right angle triangles';
45° - 45° - 90° 30° - 60° - 90°
In 45° - 45° - 90°, the adjacent is equal to the opposite
30° - 60° - 90°, there are three different sides
The longest side faces 90°, the shortest side will face the smallest angle and the intermediate will face 60°
A.
To find AB, use Pythagoras theorem;
AB² = AC² + BC²
AB² = 13² + 4²
AB² = 169 + 16 = 185
AB = √185 = 13.6
AB = 13.6
Angle A = 30°
Angle B = 60°
B.
AB² = BC² + AC²
The unknown is AC;
AC² = AB² - BC²
AC² = 5² - 4²
AC² = 9
AC = √9 = 3
Angle A = 60°
Angle B = 30°
C.
AB² = AC² + BC²
Insert the parameters and find AC;
AC² = AB² - BC²
AC² = 11² - 4.4²
AC² = 101.64
AC = √101.64
AC = 10.1
Angle A = 30°
Angle B = 60°
AC = 13