Introduction: A major topic, especially for Paper II. You must know SOH-CAH-TOA perfectly. The challenge is usually in drawing the correct diagram for word problems involving angles of elevation, depression, and bearings.

The "S Pass" Foundation (නියත S එකකට)

• Prompt 1 (Define): For a given angle θ in a right-angled triangle, define the Sine, Cosine, and Tangent ratios (SOH-CAH-TOA).

• Prompt 2 (Calculate): In a right-angled triangle, the side opposite to angle θ is 8 cm and the hypotenuse is 17 cm. Find sinθ and cosθ.

• Prompt 3 (Special Angles): Without a calculator or table, what is the exact value of tan60∘ and sin30∘?

• Prompt 4 (Use Tables): Find the value of cos54∘30′ using the trigonometric tables.

• Prompt 5 (Use Tables): Find the angle θ if tanθ=1.455.

Climbing to a "C" (C එකට පාර)

• Prompt 1 (Problem Solve): In right-angled triangle ABC, B^=90∘, AC^B=30∘ and AC = 12 cm. Find the lengths of AB and BC.

• Prompt 2 (Problem Solve): From a point 50 m away from the foot of a vertical tower, the angle of elevation to the top of the tower is 60°. Find the height of the tower.

• Prompt 3 (Problem Solve): From the top of a lighthouse 80 m high, the angle of depression of a ship at sea is 25°. How far is the ship from the foot of the lighthouse?

• Prompt 4 (Problem Solve): A ship travels 100 km on a bearing of 060°. How far North and how far East has it travelled from its starting point?

• Prompt 5 (Identity): If sinθ=53​, construct a right-angled triangle and find the values of cosθ and tanθ.

Aiming for a "B" (B ඉලක්කය)

• Prompt 1 (Two Angles): A person standing on a river bank observes a tree on the opposite bank at an angle of elevation of 60°. When he moves back 40 m, the angle of elevation becomes 30°. Find the height of the tree and the width of the river.

• Prompt 2 (Bearings): A boat sails 8 km from port A on a bearing of 040° to port B. It then sails 6 km from port B on a bearing of 130° to port C. Find the distance and bearing of C from A.

• Prompt 3 (Rider): In triangle ABC, AD is perpendicular to BC. If tanB=BDAD​ and tanC=CDAD​, show that BC=AD(tanB1​+tanC1​).

• Prompt 4 (Problem Solve): From a window 15 m high, the angle of elevation of the top of a flagpole is 30° and the angle of depression of its foot is 45°. Find the height of the flagpole.

• Prompt 5 (Synthesis): In parallelogram ABCD, AB = 12 cm, AD = 8 cm, and angle DA^B=60∘. Find the length of the diagonal BD.

Securing the "A" Distinction (A සාමාර්ථය තහවුරු කරගන්න)

• Prompt 1 (Proof): Prove that for any angle θ, sin2θ+cos2θ=1.

• Prompt 2 (Challenge): Two ships leave a port at the same time. One travels at 20 km/h on a bearing of 045° and the other travels at 15 km/h on a bearing of 315°. How far apart are they after 2 hours?

• Prompt 3 (3D Problem): A vertical pole stands at a corner of a rectangular field. The angles of elevation of the top of the pole from the two nearest corners are 45° and 60°. If the dimensions of the field are 50 m x 40 m, find the height of the pole.

• Prompt 4 (Derive): In any triangle ABC, prove the Sine Rule: sinAa​=sinBb​=sinCc​.

• Prompt 5 (Derive): In any triangle ABC, prove the Cosine Rule: a2=b2+c2−2bccosA.