Category Archives: Trigonometry

$\triangle{ABC}$ is a right triangle, with $\angle{ACB}=90^\circ$ and $\angle{BAC}=50^\circ$. Point $D$ and $E$ are on line $BC$ and $AC$ respectively, so that $\angle{BAD}=\angle{ABE}=30^\circ$. Connect $D$ and $E$, find the value of $\angle{ADE}$. Click here for the solution. Solution: Let $AD$ … Continue reading →

$\triangle{ABC}$ has a right angle at $B$, $AB = 12$, and $BC = 16$. Let $M$ be the midpoint of $AC$. Let $ω_1$ be the incircle of $\triangle{ABM}$ and $ω_2$ be the incircle of $\triangle{BCM}$. The line externally tangent to … Continue reading →