Answer:
c ≈ 6.49
A ≈ 17.9°
B ≈ 67.1°
Step-by-step explanation:
To find the length of side c, use the Cosine rule.
Cosine rule
[tex]\sf c^2=a^2+b^2-2ab \cos C[/tex]
(where a, b and c are the sides and C is the angle opposite side c)
From inspection of the given triangle:
Substitute the given values into the formula and solve for c:
[tex]\implies \sf c^2=2^2+6^2-2(2)(6) \cos 95^{\circ}[/tex]
[tex]\implies \sf c^2=4+36-24 \cos 95^{\circ}[/tex]
[tex]\implies \sf c=\sqrt{40-24 \cos 95^{\circ}}[/tex]
[tex]\implies \sf c=6.49\:\:(2\:d.p.)[/tex]
To find angles A and B, use the Sine Rule.
Sine Rule
[tex]\sf \dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}[/tex]
(where A, B and C are the angles and a, b and c are the sides opposite the angles)
From inspection of the given triangle:
- a = 2
- b = 6
- [tex]\sf c=\sqrt{40-24 \cos 95^{\circ}}[/tex]
- C = 95°
Substitute the given values into the formula:
[tex]\implies \sf \dfrac{\sin A}{2}=\dfrac{\sin B}{6}=\dfrac{\sin 95^{\circ}}{\sqrt{40-24 \cos 95^{\circ}}}[/tex]
Solving for A:
[tex]\implies \sf \dfrac{\sin A}{2}=\dfrac{\sin 95^{\circ}}{\sqrt{40-24 \cos 95^{\circ}}}[/tex]
[tex]\implies \sf A=\sin^{-1}\left(\dfrac{2\sin 95^{\circ}}{\sqrt{40-24 \cos 95^{\circ}}}\right)[/tex]
[tex]\implies \sf A=17.9^{\circ}\:\:(1\:d.p.)[/tex]
Solving for B:
[tex]\implies \sf \dfrac{\sin B}{6}=\dfrac{\sin 95^{\circ}}{\sqrt{40-24 \cos 95^{\circ}}}[/tex]
[tex]\implies \sf B=\sin^{-1}\left(\dfrac{6\sin 95^{\circ}}{\sqrt{40-24 \cos 95^{\circ}}}\right)[/tex]
[tex]\implies \sf B=67.1^{\circ}\:\:(1\:d.p.)[/tex]
Learn more about Sine Rule here:
https://brainly.com/question/28033514
https://brainly.com/question/27089170
