Find the bearing of X from Y

Given that $\sin {{60}^{\circ }}=\tfrac{\sqrt{3}}{2}\text{ and }\cos {{60}^{\circ }}=\tfrac{1}{2}$ evaluate $\frac{1-\sin {{60}^{\circ }}}{1+\cos {{60}^{\circ }}}$

An object is 6m from the base of a mast. If the angle of depression of the object from the top of the mast is 50^o, find, correct to 2 decimal places, the height of the mast

If $\cos \theta =x$and $\sin {{60}^{\circ }}=x+0.5$ ${{0}^{\circ }}<\theta <{{90}^{\circ }}$find correct to the nearest degree, the value of θ 

In the diagram TX is perpendicular to UW, $\left| UX \right|=1cm$and $\left| TX \right|=\left| WX \right|=\sqrt{3}cm$ Find $\angle UTW$

Kweku walked 8m up a slope and was 3m above the ground. If he walks 12m further up the slope, how far above the ground will he be?

In the diagram $\angle WOX={{60}^{\circ }}$, $\angle YOE={{50}^{\circ }}$and $\angle OXY={{30}^{\circ }}$what is the bearing of X from Y

If $\sin 3y=\cos 2y$ and ${{0}^{\circ }}\le y\le {{90}^{\circ }}$, find the value of y

Given that $\tan x=1$ where ${{0}^{\circ }}\le x\le {{90}^{\circ }}$ evaluate $\frac{1-{{\sin }^{2}}x}{\cos x}$

A boy looks through a window of a building and sees a man fruits on the ground 50 m away from the foot of the building. If the windows is  9m from the ground. Calculate, correct to the nearest degree, the angle of depression of the mango from windows