Search problems

3 problems match “law of sines”. Clear

Visitors search a sample. Sign in for free to search every problem. Sign in

1. Angle ACB with AB equal to CD ●●●○○ 50 ptsIn triangle $ABC$, point $D$ lies on $BC$ such that $\angle BAD = 60^\circ$, $\angle B = 20^\circ$ and $AB = CD$. Find $\angle ACB$ in degrees.
2. Sum of squared tangents in a tetrahedron section ●●●●○ 100 ptsA regular tetrahedron is intersected by a plane that is perpendicular to one of its faces and meets that face along a line $e$. The intersection lines of this plane with the other three face planes of the tetrahedron form angles $\varphi_1, \varphi_2, \varphi_3$ with $e$. Determine the value of $\tan^2 \varphi_1+\tan^2 \varphi_2+\tan^2 \varphi_3$.
3. Shortest network connecting regular pentagon vertices ●●●●○ 100 ptsA regular pentagon has side length 1 cm. Find the total length, in cm, of the shortest network of line segments that connects all five vertices of the pentagon. Give your answer in centimetres, rounded to two decimal places.