Given: ABC is a right-angled triangle, ∠B=90∘ AC=2BC,∠A=x Formula Used: The Sum of the angle of a triangle is 180∘ sin30∘=1∕2 Calculation: Let ∠C=y and BC=a So, AC=2a
In △ABC sinx=BC∕AC ⇒sinx=a∕2a=1∕2 ⇒sinx=sin30∘ ⇒x=30∘ We know that ∠A+∠B+∠C=180∘ ⇒30∘+90∘+∠C=180∘ ⇒∠C=60∘ ⇒y=60∘ ⇒y=2×30∘ From (i) ⇒y=2×x=2x ∴ The value of ∠C is 2x .