Starter Calculate the area of this triangle. Hint: Area = x b x h height = 4 x tan 64 height = 8.2 cm height 64 4cm area = x 4 x 8.2 area = 16.4 cm Calculate the area of this triangle:
7 cm 37 11 cm Why is it difficult to find the area of this triangle? Because we dont know the height. The vertices of a triangle are labelled with capital letters. The triangle shown is triangle ABC. B a
C c b A Area of a triangle = base x height Derive a formula to find the area of this triangle. Area of a triangle = base x height B c
a h C b A sin = opp sin C = h h = a sin C hyp a Area of a triangle = b x a sin C = a b sin C a b sin C = b c sin A = a c sin B
a b sin C = b c sin A = a c sin B B a C c b A Calculate the area of this triangle:
7 cm 37 11 cm Area = x 7 x 11 x sin 37= 23.17 cm Example 1: Find the area of this triangle. Give your answer to 3sf 5.8 cm 43 12.3 cm
Area = x 12.3 x 5.8 x sin 43= 24.3 cm Sometimes questions give us the area but ask us to find either angles or sides. Example 2: In triangle ABC, a = 3.6 cm, b = 4.9 cm and the area is 5 cm. Find the size of angle Hint: ifBCA. its tricky, draw a piccy! 3.6 cm 4.9 cm 5 = x 3.6 x 4.9 x sin C
0.5668 = sin C C = 34.5 Example 3: In triangle ABC, b = 13 cm, Angle CAB = 66 and the area is 100 cm. Find the length of side c. B 100 = x 13 x c x sin 66 Area = 100cm c = 16.84 cm C
66 A 13 cm Extension Use the measurements given to find the area of this quadrilateral shaped field. Give your answer to 3sf. 45m 50m 62 70
25m 60m Answers 10.69cm 26.24mm 3.90cm 44.49m 202.11cm 56 Starter
The 12-sided window is made up of squares, equilateral triangles and a regular hexagon. The perimeter of the window is 15.6m. Calculate the area of the window. B a sin C = sin A = sin B C c a b c
b A ...is the same as... c = a = b Sin C sin A sin B We can use this formula to find missing sides or angles of non-right-angled triangles Find the length of the side marked a and give your answer correct to 3 s.f. a
68 38 9.4cm a = 6.2417 a = 6.24 cm (3 s.f.) Find the size of the acute angle marked B and give your answer correct to 1 d.p. 72 B sin b = 0.7860
9.8cm 8.1cm Extension task Quadrilateral ABCD is made up of two triangles ABD and BCD. Use the sine rule to work out the area of triangle BCD. C D
3m 45 B 8m 30 A Answers How confident do you feel with this topic? 11.31cm
5.90m Write red, amber or green in your book! 9.36mm 13.89m Complete the corresponding activity 73 37 Answers 11.31cm 5.90m 9.36mm
13.89m 73 37 The angle of elevation of the top of a building measured from point A is 25o. At point D which is 15m closer to the building, the angle of elevation is 35o Calculate the height of the building. T 10o 36.5 35o B
145 25o o D 15 m Angle TDA =180 35 = 145o Angle DTA = 180 170 = 10o TD 15 Sin 25o Sin10o 15Sin 25o
TD 36.5 m Sin10 Sin 35o A TB 36.5 TB 36.5Sin 35o 20.9 m Starter Rearrange
a = b + c - 2bc cosA to make cosA the subject of the formula B a a = b + c - 2bc cosA ...is the same as... C c b
A cosA = b + c - a 2bc We can use this formula to find missing sides or angles of non-right-angled triangles Find the length of the side marked a and give your answer correct to 3 s.f. a2 = 82 + 9.62 2 x 8 x 9.6 x Cos 40o 9.6 cm a a = (82 + 9.62 2 x 8 x 9.6 x Cos
40o) 40o 8 cm a = 6.20 cm (3 sf) Find the size of the acute angle marked A and give your answer correct to 1 d.p. cosA = 6 + 4.9 - 3.2 2 x 6 x 4.9 6 cm 3.2 cm A = Cos-1 (6 + 4.9 - 3.2)
(2 x 6 x 4.9) A = 32.2 (1 dp) A 4.9 cm Extension task An AWACS aircraft takes off from RAF Waddington (W) on a navigation exercise. It flies 530 miles North to a point (P) as shown, It then turns left and flies to a point (Q), 670 miles away. Finally it flies back to base, a
distance of 520 miles. P 670 miles Find the bearing of Q from point P. cosP = 670 + 530 - 520 2 x 670 x 530 Q P = 49.7 (1 dp) Bearing = 180 + 49.7 = 229.7 530 miles
520 miles W Answers 8.03cm 5.94m 49 7.91mm 14.13cm 54