Respuesta :
By using the law of cosines the value of x is 27.6
What is the law of cosines?
The law of cosines describes the relationship between a triangle's side lengths and the cosine of its angle. The cosine rule is another name for it. According to the cosine law's assertion, if ABC is a triangle, we have:
In the equation, a² = b² + c² - 2bc cosα, a, b, and c are the triangle's sides and is the angle between b and c.
Similar to this, if β and γ are the corresponding angles between sides ca and ab, then using the Law of cosine, we have:
b² = a²+ c² - 2ac sinβ
c² = b²+ a² - 2ab cosγ
The Pythagoras theorem will be supported if any of the angles α, β, or γ is equal to 90 degrees since cos 90 = 0. As a result, the three equations above can be written as:
a²= b² + c² [if α = 90 degrees].
b² = a²+ c² [if β = 90 degrees]
c² = b² +a². [if γ = 90 degrees]
We have been given a=x b=15 and c=19 and ∠a=108°
By using the law of cosines,
a² = b² + c² - 2bc cosα
x² = 15² + 19² -2×15×19×cos108°
x² = 225 + 361 - 570cos108°
x² = 586 - 570×(-0.3090)
x² = 586 + 176.1396
x² = 762.1396
By taking square both sides
x =√762.1396
x = 27.6068
Hence x = 27.6
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