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? 16 18 19 21 law of cosines: ( a^2 = b^2 + c^2 - 2bccos(a) )

Explanation:

Step1: Identify the formula

Use the Law of Cosines \(a^{2}=b^{2}+c^{2}-2bc\cos(A)\). Here, \(b = 13\), \(c = 17\), and \(A=64^{\circ}\).

Step2: Substitute values into the formula

$$
LATEXBLOCK0
$$

Step3: Solve for \(x\)

Take the square root of \(x^{2}\), \(x=\sqrt{264.24}\approx16.26\). Rounding to the nearest whole number.

Answer:

16