+1927 In the diagram below, \angle XOY = 30^\circ and OA=15. Let B and C be points on rays \overrightarrow{OY}$ and $\overrightarrow{OX}, respectively. Find the area of triangle ABC if OB = 10 and OC = 12.
Triangle ABC is dilated to triangle A'B'C', so that the distance between corresponding sides is $1.$ Given that triangle $ABC$ has perimeter $100$, find the scale factor of the dilation.
In triangle ABC, \sin A:\sin B:\sin C=5:6:3. In triangle PQR, P = 30, Q = 60, and R = 90. What are tan P, tan Q, and tan R?
In the diagram below, Point A is \sqrt 3 units above O. Whenever Tasha moves a point, she translates the point $\sqrt 2$ units to the right. Whenever Richard moves a point, he rotates the point clockwise about point $O$ by $60^\circ.$
In one round of transformations, Tasha moves $A$ to $A',$ and then Richard moves $A'$ to $A''.$ In another round of transformations, Richard moves $A$ to $A_1,$ and then Tasha moves $A_1$ to $A_2.$ Find $A''A_2.$
As shown in the diagram, a 7 \times 2 rectangle (in black) is rotated $90^\circ$ counterclockwise around its center (i.e. the intersection of its diagonals) to reach its new position (in red). Find $\angle XYZ$ in degrees.
