find the length of side x. round to the hundredths place.

Explanation:

Step1: Apply the Law of Cosines

The Law of Cosines formula for a triangle with sides (a), (b), (c) and the angle (\theta) opposite to side (c) is (c^{2}=a^{2}+b^{2}-2ab\cos\theta). Here, let (a = 14), (b = 20), (\theta=33^{\circ}), and we want to find (x). So (x^{2}=14^{2}+20^{2}-2\times14\times20\times\cos(33^{\circ})).

Step2: Calculate the squares and cosine - value

First, (14^{2}=196), (20^{2}=400), and (\cos(33^{\circ})\approx0.8387). Then (2\times14\times20\times\cos(33^{\circ})=2\times14\times20\times0.8387 = 469.672). And (14^{2}+20^{2}=196 + 400=596).

Step3: Find (x^{2})

(x^{2}=596-469.672 = 126.328).

Step4: Find (x)

(x=\sqrt{126.328}\approx11.24).

Answer:

(11.24)