SOLUTION: The length of a rhombus is 10 cm an measured angle A is 60 degrees. Find the length of the longer diagonal AC.

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Question 191791: The length of a rhombus is 10 cm an measured angle A is 60 degrees. Find the length of the longer diagonal AC.
Answer by RAY100(1637) (Show Source):
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RHOMBUS = ALL SIDES EQUAL
f ----d.................................c
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a....................................b---e
Let abcd be rhombus
angle dcb = 60 deg
therefore angle bcd =60, angle bce = 30 deg
bce is a 30 - 60 - 90 right triangle
bc =10 (given)
be = 5 (given 1/2 of bc due to 30-60-90 proportions)
ce = 5sq rt 3 ( given 30-60-90 proportions
triangle ae-ce-ca is rt triangle with sides (10 +5 =15) - (5 sq rt 3) - diagonal (ac)
using pythagorous c^2 = a^2 = b^2

(ac)^2 = (ae)^2 + (ce)^2
ac^2 = 15^2 + (5sq rt 3)^2
ac^2 = 225 + (25*3)
ac^2 = 300
ac = sq rt 300 = 10 sq rt 3
short diagonal is bd = 5 sq rt 7 in similar fashion
bd^2= 10^2 + ( 5sq rt 3)^2 = 175