Math  /  Trigonometry

QuestionUse the Lat of Cosines to determine the indicated side xx in the following figure. (Rou x=x= \square

Studdy Solution
Calculate the values:
First, calculate 242 24^2 and 482 48^2 :
242=576 24^2 = 576 482=2304 48^2 = 2304
Then calculate the cosine term:
22448cos(39) 2 \cdot 24 \cdot 48 \cdot \cos(39^\circ)
Calculate cos(39) \cos(39^\circ) using a calculator:
cos(39)0.7771 \cos(39^\circ) \approx 0.7771
Now substitute back:
x2=576+2304224480.7771 x^2 = 576 + 2304 - 2 \cdot 24 \cdot 48 \cdot 0.7771
x2=28801790.9184 x^2 = 2880 - 1790.9184
x2=1089.0816 x^2 = 1089.0816
Finally, take the square root to solve for x x :
x1089.0816 x \approx \sqrt{1089.0816}
x33.0 x \approx 33.0
The length of side x x is approximately:
33.0 \boxed{33.0}

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