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1 In the diagram, AB = BC = 3 cm, DC = 4.5 cm, angle ABC = 90° and angle ACD = 25°. D (a) Calculate the length of AC. 4.24 cm A 4.5 cm 3 cm B 25° 3 cm C 2 The height of a vertical cliff is 450 m. The angle of elevation from a ship to the top of the cliff is 23°. The ship is x meters from the bottom of the cliff. Calculate the value of x. 1060 m (3 sig figs) 3 The diagram shows a water tower standing on horizontal ground. The height of the tower is 26.5 m. From a point A on the ground the angle of elevation to the top of the tower is 28°. Calculate, correct to the nearest meter, the distance x m. 50 m xm A 4 In the diagram, AB = BC = 3 cm, DC = 4.5 cm, angle ABC = 90° and angle ACD = 25°. (b) Calculate the area of triangle ACD. 4.03 cm2 D A 4.5 cm 3 cm B 25° 3 cm C 5 A rectangular block of wood with face ABCD leans against a vertical wall, as shown in the diagram below. AB = 8 cm, BC = 5 cm and angle BAE = 28°. Wall F C D B E 28º Ground A Find the vertical height of C above the ground. 8.17 cm 6 The diagram shows a cuboid 22.5 cm by 40 cm by 30 cm. (a) Calculate the length of AC. 37.5 cm H E G F (b) Calculate the size of angle GAC. 40 cm 46.8° D C 30 cm A 22.5 cm B 7 In the diagram, PQRS is the square base of a solid right pyramid with vertex V. The sides of the square are 8cm, and the height VG is 12cm. M is the midpoint of QR. Diagram not to scale (a) Calculate the length of VM. 12.6 cm (b) Find the angle between the face VQR and the base of the pyramid. (angle between VM and MG) 71.6° (or 72.2° or 71.5°) V VG = 12 cm P Q G S 8 cm 8 cm M R 8 The diagram shows the plan of a playground with dimensions as shown. C Calculate the area of triangle ABC 48 m 117º A B 57 m 1220 m2 (3 s.f.) 9 The following diagram shows the rectangular prism ABCDEFGH. The length is 5 cm, the width is 1 cm, and the height is 4 cm. C Find the length of CF. B H G 6.48 cm D A E F Diagram not to scale 10 The diagram shows a point P, 12.3 m from the base of a building of height h m. The angle measured to the top of the building from point P is 63°. Calculate the height h of the building. 24.1 m hm P 63° 12.3 11 OABCD is a square based pyramid of side 4 cm as shown in the diagram. The vertex D is 3 cm directly above X, the centre of square OABC. M is the midpoint of AB. D (a) Calculate the length of DM. 3.61 cm Diagram not to scale (b) Calculate the angle between DM and XM. B C 56.3° X M (or 56.2° or 56.4°) O A In the diagram below ABEF, ABCD and CDFE are all rectangles. AD = 12cm, DC = 20cm and DF = 5cm. M is the midpoint of EF and N is the midpoint of CD. 12 E (a) Calculate the length of AM 16.4 cm B M (b) Calculate the angle between AM and AN 17.8° A 12 cm F N 5 cm D C 13 Determine the area of: 7.3km 38° 9.4 km 21.1 km2 14 A triangle has sides of length 7cm and 13cm and its area is 42cm2. Find the size of its included angle. 67.4° 15 In the diagram, AB = BC = 3 cm, D DC = 4.5 cm, angle ABC = 90° and angle ACD = 25°. A (c) Calculate the area of quadrilateral ABCD. 8.53 4.5 cm cm2 3 cm B 25° 3 cm C • When a 5 foot 4 inch tall person casts a 4 foot 2 inch shadow, what is the angle of elevation of the sun? • Steps to the entrance of a school rise a total of 2 feet. They are to be torn out and replaced by a wheelchair ramp, inclined at 12°. How long (along the slant) is the ramp? The measure of angle CBA is 22°. The measure of angle DBA is 47°. Find the length of CA. D 48 cm C B A BA is 71.8 cm and so AC is 29.0 cm • The length of the base of an isosceles triangle is 72.5 inches and each base angle has a measure 46.8°. Find the length of each of the two equal sides of the triangle. 53.0 inches Homework • Review Set 10A, pg349 – #1-8 • Review Set 10B, pg351 – #1-7