Question

question 1
a parallelogram has sides of lengths 7 and 6, and one angle is 34°.
what is the length of the smaller diagonal?
length = units
what is the length of the longer diagonal?
length = units
enter your answer as a decimal; your answer should be accurate to 3 decimal places.
question help: message instructor

Explanation:

Step1: Recall the law of cosines

The law of cosines is \(c^{2}=a^{2}+b^{2}-2ab\cos C\). For a parallelogram with sides \(a = 6\), \(b = 7\), and angle \(C=34^{\circ}\), the smaller diagonal \(d_{1}\) is given by \(d_{1}^{2}=6^{2}+7^{2}-2\times6\times7\times\cos(34^{\circ})\).

Step2: Calculate the smaller diagonal

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The larger - angle of the parallelogram is \(180^{\circ}-34^{\circ}=146^{\circ}\). For the longer diagonal \(d_{2}\), using the law of cosines \(d_{2}^{2}=6^{2}+7^{2}-2\times6\times7\times\cos(146^{\circ})\)

Step3: Calculate the longer diagonal

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Answer:

length of the smaller diagonal: \(3.920\) units
length of the longer diagonal: \(12.435\) units