find the value of the unknown in rhombus
Answers
Answer:
If the area of the rhombus is known, say A (=100 sq cm), we can fid the angles of the rhombus depending on additional information as given below:
a. If the sides are say S (=20 cm)
100 = (20*20/2)*sin A, or
sin A = 2*100/400 = 0.5.
So A = 30 deg, and the other adjacent angle is 150 deg.
b. If the shorter diagonal, say AC = 10 cm, then the longer diagonal = 2x100/10 = 20 cm.
The smaller angle of the rhombus = 2*arc tan (10/2)/(20/2)
= 2x26.565
= 53.130 deg
The other adjacent angle is 126.870 deg.
c. If the distance between opposite sides, say 8 cm, then each side of the rhombus = 100/8 = 12.5 cm. Then the smaller angle of the rhombus = arc sin 8/12.5 = 39.79 deg. and the adjacent angle is 140.21 deg.
Step-by-step explanation:
hope my answer help you