Solution of Triangle

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