Answer:
A = 137° a = 14 cm
B = 26° b = 9 cm
C = 17° c = 6 cm
Step-by-step explanation:
Cosine rule
[tex]c^2=a^2+b^2-2ab\cos (C)[/tex]
[tex]\implies C=\cos^{-1}\left(\dfrac{c^2-a^2-b^2}{-2ab}\right)[/tex]
where:
- c is the side opposite angle C
- a and b are the sides with C as the included angle.
Given:
- a = 14 cm
- b = 9 cm
- c = 6 cm
[tex]\implies C=\cos^{-1}\left(\dfrac{6^2-14^2-9^2}{-2(14)(9)}\right)[/tex]
[tex]\implies C=\cos^{-1}\left(\dfrac{241}{252}\right)[/tex]
[tex]\implies C=16.99128694..\textdegree[/tex]
Sine Rule
[tex]\sf \dfrac{sinA}{a}=\dfrac{sinB}{b}=\dfrac{sinC}{c}[/tex]
(where A, B and C are the angles and a, b and c are the sides opposite the angles)
[tex]\sf \implies \dfrac{sinB}{9}=\dfrac{sin(16.991..)}{6}[/tex]
[tex]\sf \implies B=sin^{-1}\left(\dfrac{9sin(16.991..)}{6}\right)=25.99797699...\textdegree[/tex]
Sum of interior angles of a triangle = 180°
⇒ ∠A + ∠B + ∠C = 180°
⇒ ∠A = 180° - 25.997...° - 16.9912...°
⇒ ∠A = 137.0107361...°
