In the figure, △CBD lies on a horizontal plane with CB = 27m, BD = 36m and CD = 45m. AB = 13m is perpendicular to the plane CBD. Find the angle between AC and the plane CBD, correct to the nearest degree.

ABCDEFGH is a rectangular box with AB = 18cm, BC = 12cm and AE = 10cm. Find cos∠EAG.

In the figure, PQRS is a tetrahedron. The base △PQR lies on a horizontal plane. Q is vertically below S. ∠PQR = 90°, ∠QPS = 45° and ∠QRS = 60°. Find cos∠RPS.

T is a point vertically above O on a horizontal ground at height h. A and B are two points on the ground with ∠AOB = 150°. The angle of elevation of T from A is 30° and from B is 60°. Express AB in terms of h.

ABCDEFGH is a cube where ABCD is the bottom face and EFGH is the top face. Let α be the angle between △BEG and △BEH. Find cos α.

ABCD is a regular tetrahedron with all edges of length 6. Find its volume.

ABCDEF is a right prism where △ABC and △DEF are congruent triangles with AB = 9cm and AC = 15cm. AD = 12cm. P is on AD with AP = 4cm. Find ∠BPD, correct to the nearest degree.

VABCD is a right pyramid with square base ABCD. V is directly above the centre of the base. AB : VA = 5 : 4. Find cos of the angle between faces VAB and the base.

In △ABC, ∠B = 90°. AB = 24, BC = 45 and AC = 51. Find cos∠C.

In the figure, AC ⊥ BD. AC = 24 and AB = 51. Find sin∠ABC.

In quadrilateral ABCD, ∠ABC = 30°, AB = 13 and BC = 10. Find AC.

In △ABC, AB = 13, BC = 10 and ∠ABC = 30°. Find cos∠ACB.

A ship sails from A on a bearing of 090° for 153m to B, then turns to a bearing of 120° and sails 179m to C. Find the distance AC, correct to the nearest metre.

Simplify cos(180° − θ) × tan(360° + θ).

How many roots does 2sin²x − 3sin x + 1 = 0 have in 0° ≤ x < 360°?

The figure shows the graph of y = a + b cos cx for 0° ≤ x ≤ 360°. The maximum value is 1 and the minimum value is -1. Find a.