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The value of x in the triangle using the cosine rule is 22.1 degrees.
An equation is an expression that shows the relationship between two or more numbers and variables.
Cosine rule is used to show the relationship between the sides and angles of a triangle. It is given by:
c² = a² + b² - 2ab cos C
Where a, b, c are the sides and C is the angle opposite side c.
Using cosine rule:
8² = 14² + 19² - 2(14)(19) * cos(x)
cos(x) = 0.9267
x = 22.1°
The value of x in the triangle using the cosine rule is 22.1 degrees.
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Using the law of Cosines, the value of x to the nearest tenth is 77.8
From the question, we are to determine the value of x
Using the law of Cosines
c² = a² + b² - 2ab cos C
c is the unknown side length
a and b are the given side lengths
and C is the included angle
From the given information,
a = 63
b = 62
C = 142°
Then,
x² = 63² + 61² -2×63×61 cos 142°
x² = 3969 + 3721 -7686(-0.788)
x�� = 7690 + 6056.568
x² = 13746.569
x = √13746.569
x = 77.8
Hence, the value of x to the nearest tenth is 77.8
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