O P Malhotra, S K Gupta and, Anubhuti Gangal Solutions for Exercise 3: Exercise

Find the value of $\frac{5{\sin }^{2}30°+{\cos }^{2}45°-4{\tan }^{2}30°}{2\sin 30°\cos 30°+\tan 45°}$.

A pole $15 \mathrm{m}$ long rests against a vertical wall at an angle of $60°$ with the ground. Calculate how high up the wall will the pole reach ?

Without using tables, in triangle $\mathrm{ABC}$, right-angled at $\mathrm{C}$, given $\mathrm{A}=30°$ and $\mathrm{c}=40$, find the remaining sides and an angle ?

Without using tables, in triangle $\mathrm{ABC}$, right-angled at $\mathrm{C}$, given $B=60°$ and $\mathrm{c}=15$, find the remaining sides and an angle ?

Without using tables, in triangle $\mathrm{ABC}$, right-angled at $\mathrm{C}$, given $A=45°$ and $\mathrm{a}=7$, find the remaining sides and an angle ?

If $4{\sin }^2\mathrm{\theta }-1=0$ and angle $\mathrm{\theta }$ is less than $90°$; find the value of $\mathrm{\theta }$ and hence the value of ${\cos }^2\mathrm{\theta } + {\tan }^2\mathrm{\theta }$.

In a right triangle $\mathrm{ABC}$, right angled at $\mathrm{C}$, if $\angle \mathrm{B} = 60°$ and $\mathrm{AB}=15$ units, find the remaining angle and sides.

In a rectangle $\mathrm{ABCD}, \mathrm{AB}=20 \mathrm{cm}, \angle \mathrm{BAC}=60°$, calculate side $\mathrm{BC}$ and diagonals $\mathrm{AC}$ and $\mathrm{BD}$.