### Solution of Triangle

goals
Find the approximate value of $\angle{A}$ in $\triangle{ABC}$ if $8\angle{A}=9\angle{B}=4\angle{C}$.
The sides of a triangle are $\sin \alpha, \cos \alpha$ and $\sqrt {1 + \sin \alpha \cos \alpha}$ for some $0 < \alpha < \dfrac {\pi}{2}$. Then the greatest angle of the triangle is
If $x,8$ and $12$ are the sides of a triangle then,

$A$ balloon is observed simultaneously from three points $A,\ B,\ C$ due west of it on a horizontal line passing directly underneath it. lf the angular elevations at $B$ and $C$ are respectively twice and thrice that at$A$and if $AB=220$ metres and $BC=100$ metres, then the height of the balloon from the ground is

$A$ tree stands vertical, on the hill side, which makes an angle of $22^{0}$ with the horizontal. From the point $35$ meters directly down the hill from the base of the tree, the angle of elevation of the top of the tree is $45^{0}$. Then the height of the tree (Given $\sin 22^{0}=0.3746, \cos 22^{ } =0.9276$ from tables) is