Right-angled Trigonometry

Right-angled Trigonometry Opposite A

Right-angled Trigonometry Hypotenuse Opposite A

Right-angled Trigonometry Hypotenuse Opposite A Adjacent

Right-angled Trigonometry Opp Hyp A Adj

Right-angled Trigonometry Opp Hyp A Adj

Right-angled Trigonometry Opp Hyp A Adj

Right-angled Trigonometry Opp Hyp A Adj The Old Arab

Right-angled Trigonometry Opp Hyp A Adj The Old Arab Sat On His

Right-angled Trigonometry Opp Hyp A Adj The Old Arab Sat On His Camel And Hiccupped

Calculate the length of PQ in the triangle PQR Example Calculate the length of PQ in the triangle PQR P R 52 cm 32 Q

Calculate the length XY in the triangle XYZ Example Calculate the length XY in the triangle XYZ X Y 59 4.6 cm Z

Calculate the length of BC in the triangle ABC. Example Calculate the length of BC in the triangle ABC. B 5 cm 24 A C

Example A surveyor, P, is 1000m away on horizontal ground from the foot of a radio mast, QR. From P the angle of elevation of the top, R, of the mast is 20. Find the height of the mast. Assume the surveyor’s height to be negligible.

Example From the top of a vertical cliff 100m high the angle of depression of a boat out at sea is 32. How far is the boat from the foot of the cliff?

Example Calculate the size of angle A in the triangle ABC 4 cm A C 6 cm

Find the size of angle x in each of the following (i) Example Find the size of angle x in each of the following (i) 1.2 cm x 4.7 cm

10 cm 3.7 cm x (ii)

7 cm 12 cm x (iii)

Calculate the size of angle PQR in the triangle below. Example Calculate the size of angle PQR in the triangle below. 8 cm 6 cm P R

Example The road from village A runs due West for 5 miles to a fort B. A television mast is due South of B and 4 miles from B. Find the distance and bearing of the mast from A.

Example The figure is a pyramid on a square base ABCD. The edges of the base are 30cm long and the height, EH, of the pyramid is 42cm. Find a) the length of AC b) the angle EAH E C D B A H

(iii) the total surface area of the prism. Example ABCDEF is a prism with a triangular cross-section. , BC = 8m, AB = 6m and CD = 20m. Find (i) AC (ii) BD (iii) the total surface area of the prism. A F E C B D