Question

Each side of a rhombus is 30 units long. One diagonal makes a 25 degree angle with a side. What is the length of each diagonal to the nearest tenth of a unit?

Answer 1

25.4 units

54.4 units

Explanation:

Given that,

length of each side of rhombus = 30 units

interior angle = 25 x 2

= 50°

other interior angle = (360-(50x2)) / 2 = 130°

Formula to use

c² = a² + b² - ab cosC

First diagonal

√(30² + 30² - 2*30*30*cos 50)

= 25.35 u

Second diagonal

√(30² +30² - (2*30*30*(cos 130)))

= √(1800-1800cos130)

= 54.37 units