In a right-angled triangle ABC, with B^=90∘, AB = 8 cm, BC = 6 cm, and AC = 10 cm. Find the values of sin C, cos C, and tan C.

If sin θ=135​, find the values of cos θ and tan θ.

Using the values for special angles, find the value of 2 sin 30∘ cos 30∘.

Using trigonometric tables, find the value of tan 48∘ 23′.

Using trigonometric tables, find the angle θ if cos θ=0.5175.

A vertical post 12 m high casts a shadow of length 123​ m. Find the angle of elevation of the sun.

From the top of a cliff 100 m high, the angle of depression of a boat at sea is 35°. How far is the boat from the foot of the cliff?

In triangle PQR, Q^​=90∘, PQ = 10 cm and PR^Q=42∘. Calculate the length of PR.

A ship sails 200 km on a bearing of 120°. How far south and how far east is it from its starting point?

Show that cos θsin θ​=tan θ.

Find the value of x in the given figure, where AB^C=90∘, BC = 20, AD^B=30∘ and AC^B=45∘.

Two observers are 500 m apart on a straight horizontal road. They observe a balloon in the air between them. The angles of elevation from the observers are 60° and 30°. Find the height of the balloon.

A man observes the top of a tower from a point on the ground and finds the angle of elevation to be 30°. He walks 40 m towards the tower and finds the angle of elevation to be 60°. Find the height of the tower.

From a point A, a point B is 10 km away on a bearing of 070°. From B, a point C is 12 km away on a bearing of 160°. Find the shortest distance between A and C.

In triangle ABC, AD is perpendicular to BC. Prove that AB2+CD2=AC2+BD2.