Trigonometry: right-angled triangles, elevation and depression

Question 1 of 10

sin 30° equals

Question 2 of 10

sin² θ + cos² θ equals

Question 3 of 10

cos 60° equals

Question 4 of 10

In a right-angled triangle, the hypotenuse is 30 cm and one angle is 50°. Find the side opposite this angle, to 1 decimal place.

Question 5 of 10

The angle of elevation of A from B equals the angle of depression of B from A because they are

Question 6 of 10

In a right-angled triangle, the side opposite θ is 9, the adjacent side is 40 and the hypotenuse is 41. Write tan θ as a fraction: ___

Question 7 of 10

In a right-angled triangle, the side opposite θ is 8, the adjacent side is 15 and the hypotenuse is 17. Write cos θ as a fraction: ___

Question 8 of 10

A man stands 30 m from the foot of a building. The angles of elevation of the bottom and top of a flagpole on the roof are 35° and 55°. Find (a) the height of the building, (b) the height to the top of the flagpole, (c) the length of the flagpole, each to 1 decimal place.

Question 9 of 10

A man stands 30 m from the foot of a building. The angles of elevation of the bottom and top of a flagpole on the roof are 35° and 45°. Find (a) the height of the building, (b) the height to the top of the flagpole, (c) the length of the flagpole, each to 1 decimal place.

Question 10 of 10

From the top of a 20 m cliff, the angle of depression of a boat is 45°. How far is the boat from the foot of the cliff, to 1 decimal place?