Triangles

$ABC$ is a triangle where the side $b$ is $74\mathrm{cm}$ long and the angle $\alpha ={60}^{\circ }$. Find the length of its side $c$ if you know that the area of the triangle is $720.9{\mathrm{cm}}^2$.

An observer was watching an approaching plane flying at a height of $3000\mathrm{m}$ in a straight line with constant velocity. At the first moment of measurement the observer saw the plane to be at an angle of elevation of ${25}^{\circ }$. After $10$ seconds the angle of elevation changed to ${35}^{\circ }$. What was the speed of the plane? Round the result to ones.

The distance between the places $A$ and $C$ on a straight road is $300\mathrm{m}$. There is a balloon $B$ above the road between the places $A$ and $C$. See the picture. The angles of elevation from the places $A$ and $C$ to the balloon $B$ are ${20}^{\circ }$ and ${40}^{\circ }$ respectively. What is the height $h$ of the balloon?

What is the height of a computer screen if the ratio of its width and height is $16:9$ and the computer has $23$-inch monitor? Round the result to two decimal places. ($1$ inch=$2.54\mathrm{cm}$)