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Tpy6a [65]
2 years ago
10

Iam struggling with this one someone please help me:(

Mathematics
1 answer:
Phantasy [73]2 years ago
3 0

Answer:

x = 26.244

Step-by-step explanation:

Let the angle opposite the side of length 15 be A and the angle opposite the side with length 18 be B

if a is the side with length 18 and b is the side with length 15

then the relationship between the two know sides a and b and the included angle C is given by the law of cosines

x^2 = a^2 + b^2 - 2ab \cos(C)

x^2 = 18^2 + 15^ 2 -  2\cdot18\cdot15\cdot\cos(105)

x^2 = 324 + 225 -  540cos(105)

cos(105) = -0.2588

x^2 = 324 + 225 -540(-0.2588)\\

324 + 225 = 549

(-540)(-0.2588) = - 139.75

x^2 = 549 - (- 139.75) = 688.75

x^2 = 549 +  139.75 = 688.75

x = \pm\sqrt{688.75} = \pm26.244

Since x cannot be negative,

x = 26.244  Answer

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