Respuesta :
use cosine rule to find b
b^2 = 6^2 + 11^2 - 2*6*11cos 109 = 199.97
b = 14.1 to nearest tenth.
now use sine rule to find the value of < A
14.14 / sin 109 = 6 / sin A
<A = 24 degrees
<C = 180 - 24 - 109 = 47 degrees
Its A
b^2 = 6^2 + 11^2 - 2*6*11cos 109 = 199.97
b = 14.1 to nearest tenth.
now use sine rule to find the value of < A
14.14 / sin 109 = 6 / sin A
<A = 24 degrees
<C = 180 - 24 - 109 = 47 degrees
Its A
Answer:
Option A is correct.
Step-by-step explanation:
Given: a = 6 , c = 11 , B = 109°
To find : b , ∠A , ∠C
We use Law of cosine and Law of sines.
Law of Cosine used for calculating one side of a triangle when the angle opposite and the other two sides are known.
b² = a² + c² - 2ac.cos B
Law of Sines is a rule relating the sides and angles of any triangle.
[tex]\frac{a}{sin\,A}=\frac{b}{sin\,B}=\frac{c}{sin\,C}[/tex]
Using Law of Cosines, we get
b² = 6² + 11² - 2 × 6 × 11 × cos 109
b² = 199.97
b = 14.1 (nearest tenth)
Now using Law of sines, we get
[tex]\frac{a}{sin\,A}=\frac{b}{sin\,B}[/tex]
[tex]\frac{6}{sin\,A}=\frac{14.1}{sin\,109}[/tex]
[tex]sin\,A=\frac{0.95}{14.1}\times6[/tex]
[tex]A=sin^{-1}\,(0.404)[/tex]
∠ A = 23.8° = 24° (nearest degree)
Using Angle sum property of triangle,
∠A + ∠B + ∠C = 180°
∠C = 180 - (24 + 109)
∠C = 47°
Therefore, Option A is correct.
