UPSC CDS 1 2022 Math Paper

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=2aIn △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 .