Question

In a triangle ∠A = 55⁰, ∠B = 15⁰, ∠C = 110⁰. Then c² – a² is equal to –

• A. ab
• B. 2ab
• C. –ab
• D. None of these

Answer 1

Answer: (A)

ab

Answer 2

$\frac { \mathrm { c } } { \sin 110 ^ { \circ } }$ = = = k

Now c² – a² = k² sin² 110⁰ – k² sin² 55⁰

= k² (sin 110⁰ + sin 55⁰) (sin 110⁰ – sin 55⁰)

= k² $\left( 2 \sin \frac { 165 ^ { \circ } } { 2 } \cos \frac { 55 ^ { \circ } } { 2 } \right)$ $\left( 2 \cos \frac { 165 ^ { \circ } } { 2 } \sin \frac { 55 ^ { \circ } } { 2 } \right)$

= k² sin 165⁰ sin 55⁰

= (k sin 55) (k sin 15)

= ab.