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Rashid [163]
3 years ago
5

One angle of a rhombus measures 102°, and the shorter diagonal is 4 inches long. Approximately how long is the side of the rhomb

us? (Hint: Diagonals of a rhombus bisect the angles.)
2 in.
3 in.
4 in.
5 in.
Mathematics
1 answer:
liq [111]3 years ago
7 0

Answer:

Approximately 3 inches.

Step-by-step explanation:

The shorter diagonal will bisect the 102 degree angle. so we have a triangle  with base angles of 51, vertex 180 - 102 = 78 degrees and base length 4 inches.

Applying the Sine Rule:

4 / sin 78 = x / sin 51  where x = the length of the  side of the rhombus.

x = 4 * sin 51 / sin 78

= 3.17 inches.

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(
x
−
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Distribute:
=
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2
+
−
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x
+
9
+
2
Combine Like Terms:
=
x
2
+
−
6
x
+
9
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