Question

a parallelogram has side lengths of 4 and 6 and an angle of measure 55°. what is x, the length of the diagonal, to the nearest whole number? 3 5 6 7 law of cosines: a² = b² + c² - 2bccos(a)

Explanation:

Step1: Apply Law of Cosines

$x^2 = 4^2 + 6^2 - 2 \cdot 4 \cdot 6 \cdot \cos(55^\circ)$

Step2: Calculate squares and product

$x^2 = 16 + 36 - 48 \cdot \cos(55^\circ)$

Step3: Compute cosine value

$\cos(55^\circ) \approx 0.5736$

Step4: Calculate remaining terms

$x^2 \approx 52 - 48 \cdot 0.5736 \approx 52 - 27.53 \approx 24.47$

Step5: Find square root

$x \approx \sqrt{24.47} \approx 4.95$

Step6: Round to nearest whole number

$x \approx 5$

Answer:

B. 5