From the top of a tower of $50 \mathrm{m}$ high, Neha observes the angles of depression of the top and foot of another building to be $45°$ and $60°$ respectively. Find the height of the building to the nearest whole number (in $\mathrm{m}$). Assume $\sqrt{3}=1.732$.

Solve for $\mathrm{\theta }$, $0°<\mathrm{\theta }<90°$, if $2\mathrm{cos\theta }=1$.

For the given figure $BC=20 \mathrm{cm}$ and $\angle A=30°$, then $AB=$_____ and $AC=$ _____

Evaluate

$\frac{\sin 30°+\tan 45°-\cos ec 60°}{sec 30°+\cos 60°+cot 45°}$

Find the value of $x (0°<x<90°)$ in degrees in $\sin 2x=\sin 60°\cos 30°-\cos 60°\sin 30°$.

If $\sqrt{3}\tan \theta =1 \& \theta$ is acute, find the value of $\sin 3\theta +\cos 2\theta$.

$\tan \left(A+B\right)=\sqrt{3}$

$\tan \left(A-B\right)=\frac{1}{\sqrt{3}}$

$0°<\mathrm{A}+\mathrm{B}\le 90°$; $A>B$

find the value of $A$ and $B$

Evaluate 

$\frac{5{\cos }^{2}60°+4{\sec }^{2}30°-{\tan }^{2}45°}{{\sin }^{2}30°+{\sin }^{2}60°}$