In the right - angled \(\Delta {\rm{ABC}}\). Find the exact length of AD

Find the exact length of \(AB\).

Find the smallest angle.

Find the length of AC.

Find the \(\angle {\rm{ABC}}\).

Find the length of AC.

Find the area of the \(\Delta {\rm{ABC}}\), given that \(\angle {\rm{ABC}}\)=\({\rm{59}}^\circ \), \(AB = 7\) and \(CB = 6\).

In \(\Delta {\rm{PQR}}\), \(PQ = 6\), \(PR = 9\), \(\angle {\rm{PRQ}}\), \({\rm{24}}^\circ \). Find \(\angle {\rm{PQR}}\).

In \(\Delta {\rm{LMN}}\), \(LM = 5\), \(MN = 8\) and \(\angle {\rm{MLN}}={\rm{62}}^\circ \). Find \(\angle {\rm{LNM}}\).

The angle of depression from the top of a cliff to a small boat, 800 m from the base of the cliff is \({\rm{6}}^\circ \). Find the height of the cliff.

A ship travels from Port A for 6 nm on a bearing of \({\rm{030}}^\circ \) to Port B. It then turns and travels 5 nm to Port C on a bearing of \({\rm{120}}^\circ \). Find the distance AC.

Find the exact value of \(\sin 240^\circ \)

Find the exact area of a sector of a circle with radius 6cm and an angle of  \(\dfrac{\pi }{3}\) radians subtended at the centre.

In the adjacent 3D diagram, \(\angle {\rm{BDC}}={\rm{90}}^\circ \), \({\rm{AD}} \bot {\rm{DC}}\) and \({\rm{AD}} \bot {\rm{BD}}\). Find the length of AD.

Express \({\rm{315}}^\circ \) in radians.

In the adjacent 3D diagram.\(\angle {\rm{BDC}}={\rm{90}}^\circ \), \({\rm{AD}} \bot {\rm{DC}}\) and \({\rm{AD}} \bot {\rm{BD}}\). Find the exact length of BC.

The area of a sector of a circle is \({\rm{12 }}\,{\rm{cm^2}}\). If the radius of the circle is 3 cm, find the angle subtended at the centre.

Find the exact area of a minor segment of a circle with radius 2 cm and angle subtended is \(\dfrac{\pi }{3}\).

Find the exact area of a major segment of a circle with radius 2 cm and angle subtended is \(\dfrac{\pi }{4}\).

\(1 - \cos \theta \sin \left( {\dfrac{\pi }{2} - \theta } \right)=\)

\(\dfrac{{1 + \cot \theta }}{{{\rm{cosec}}\theta }}=\)

Solve for \(0 \le x \le 2\pi \), \({\rm{4}}\sin x=3\,{\rm{ cosec }}\,x\)

Solve for \(0 < \theta < 360^\circ \) , \(6\,{\tan ^2}\,\theta =5\sec \theta \)