Answer:
1) a = 16.38 (nearest hundredth)
b = 11.47 (nearest hundredth)
2) b = 14.14 (nearest hundredth)
c = 15.36 (nearest hundredth)
Step-by-step explanation:
Sine Rule
[tex]\sf \dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}[/tex]
(where A, B and C are the angles and a, b and c are the sides opposite the angles)
Question 1
The interior angles of a triangle sum to 180°
⇒ m∠B = 180° - 90° - 55° = 35°
Given:
- A = 55°
- B = 35°
- C = 90°
- c = 20
[tex]\implies \sf \dfrac{a}{\sin 55}=\dfrac{b}{\sin 35}=\dfrac{20}{\sin 90}[/tex]
[tex]\implies \sf a=\dfrac{20\sin 55}{\sin 90}=16.38304089...[/tex]
[tex]\implies \sf b=\dfrac{20\sin 35}{\sin 90}=11.47152873...[/tex]
Question 2
The interior angles of a triangle sum to 180°
⇒ m∠B = 180° - 90° - 23° = 67°
Given:
- A = 23°
- B = 67°
- C = 90°
- a = 6
[tex]\implies \sf \dfrac{6}{\sin 23}=\dfrac{b}{\sin 67}=\dfrac{c}{\sin 90}[/tex]
[tex]\implies \sf b=\dfrac{6\sin 67}{\sin 23}=14.13511419...[/tex]
[tex]\implies \sf c=\dfrac{6\sin 90}{\sin 23}=15.35582799...[/tex]
