Question

a parallelogram has side lengths of 13 and 17 and an angle that measures 64°. what is x, the length of the diagonal, to the nearest whole number? law of cosines: $a^{2}=b^{2}+c^{2}-2bc\cos(a)$

Explanation:

Step1: Apply Law of Cosines

$x^2 = 13^2 + 17^2 - 2 \times 13 \times 17 \times \cos(64^\circ)$

Step2: Calculate squares and product

$13^2=169$, $17^2=289$, $2 \times 13 \times 17=442$

Step3: Compute cosine term

$\cos(64^\circ) \approx 0.4384$, $442 \times 0.4384 \approx 193.77$

Step4: Solve for $x^2$

$x^2 \approx 169 + 289 - 193.77 = 264.23$

Step5: Find square root

$x \approx \sqrt{264.23} \approx 16$

Answer:

A. 16