Topic 3.2: Trigonometry: Right and Non-Right Triangles Questions

In triangle ABC, AB = 8 cm, angle A = 50° and angle B = 70°. Which formula correctly starts the calculation of BC?

Which trigonometric ratio connects the opposite side and the adjacent side?

A tree casts a shadow of length 15 m. The angle of elevation from the tip of the shadow to the top of the tree is 38°. Find the height of the tree.

In right triangle PQR, angle Q = 90°, PQ = 7 cm and PR = 25 cm. (a) Find the length QR. (b) Find the angle QPR. (c) Find the angle PRQ.

Area of triangle formula using two sides and included angle: if two sides are 5 and 8, and the included angle is 30°, what is the area?

A ramp is built to give access to a building. The ramp is 6 m long and reaches a door that is 0.8 m above the ground. Find the angle the ramp makes with the horizontal.

A right triangle has hypotenuse 20 cm and one angle of 55°. Find the lengths of both legs.

In a right-angled triangle, the side opposite to angle θ is 5 and the hypotenuse is 13. What is sin θ?

A zip-wire runs from a platform at height 12 m to the ground. The wire makes an angle of 18° with the horizontal. Find the length of the wire.

Points A and B are 6.36 m apart in a park. Odette stands at point O, with OA = 25.9 m and AÔB = 10°. (a) Calculate the size of angle ABÔ. (b) Calculate the area of triangle AOB.

Khemil stands at K, which is 12 m from A. Angle KÂB = 45°. AB = 6.36 m. Calculate the distance KB.

In triangle ABC, a = 9, b = 12 and C = 115°. Find the length of side c.

In triangle XYZ, x = 5, y = 7 and z = 9. Find angle Y.

A triangular garden has vertices at A, B, C. The owner knows AB = 14 m, BC = 11 m and angle B = 48°.

A ladder leans against a wall. The ladder is 5 m long and the foot is 2 m from the wall. What angle does the ladder make with the ground?

In right triangle ABC with right angle at C, tan A = 3/4. If BC = 6 cm, what is AB?

A right triangle has one angle of 35° and the side adjacent to this angle is 12 m. What is the length of the hypotenuse?

A rope runs from the top F of a vertical pole to the ground at point A. F is at (0, 0, 5.8) and A is at (3.2, 4.5, 0). All units are in metres. (a) Find the horizontal distance from the base of the pole to A. (b) Find the angle FAO that the rope makes with the ground.

A surveyor measures a plot of land in the shape of a right triangle. The hypotenuse is 85 m and one acute angle is 42°. Find the area of the plot.

When should you use the cosine rule instead of the sine rule?