3D Geometry
Line x=y=z Intersecting Trigonometric Planes
nta_pyq_2023_apr
Grade 12
Question:
Line $x=y=z$ intersects $x\sin A+y\sin B+z\sin C-18=0=x\sin2A+y\sin2B+z\sin2C-9$ where $A,B,C$ are angles of $\triangle ABC$. Then $80\!\left(\sin\frac{A}{2}\sin\frac{B}{2}\sin\frac{C}{2}\right)$ is equal to _________
Step-by-Step Solution
Key Concept: On $x=y=z$: $t(\sin A+\sin B+\sin C)=18$ and $t(\sin2A+\sin2B+\sin2C)=9$. Divide.
$5$.
Correct Answer: 5