Respuesta :
Answer:
x = 27.57 in to the nearest hundredth.
Step-by-step explanation:
The longer diagonal is opposite the obtuse angle.
Also as it is a rhombus all sides = 14 in.
Use the Cosine Rule:
x^2 = 14^2 + 14^2 - 2*14^2 cos 160
x^2 = 760.36
x = sqrt 760.36
x = 27.57 in.
The length of the longer diagonal of the rhombus with side 14 inches is;
27.57 inches.
We are told that the side of the rhombus is 14 inches.
Now, a rhombus has all its' 4 sides equal.
This means that the obtuse angle is the angle formed by 2 sides.
Thus, we can find the length of the diagonal using cosine rule. If the diagonal is c, then;
c² = 14² + 14² - 2(14 × 14) cos 160
c² = 196 + 196 + 368.3595
c² = 760.3595
c = √760.3595
c = 27.57 inches
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