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Simplifying Identities
Solving Trig Equations
Sine Rule
Area Formula
Cosine Rule
100
(sec A)(cos A)
1
100
Solutions 0 to 360 degrees for sin A = √3 / 2
60 and 120 degrees
100
In a triangle, angle A is 45 degrees, angle B is 30 degrees, side CB is 5 cm. What is the exact length of side AC?
5 sq. rt. 3 / sq. rt. 2
100
Two sides of a triangle are 7 and 9 units, the angle included between them is 120 degrees.
27.3 square units
100
Two sides of a triangle are 7 and 3 units long, the angle included between them is 52 degrees. How long is the third side?
5.70
200
(tan A)(cos A)
sin A
200
Solutions 0 to 360 degrees for cos x = - 1/2
120 and 240 degrees
200
In triangle ABC, a = 4 cm, b, = 7 cm and angle B = 80 degrees. Calculate the size of angle A and angle C and the length of side c. State to 2 d.p.
34.25 degrees, 65.75 degrees and 6.48 cm
200
Two sides of a triangle are 7 and 9 units, the angle included between them is 120 degrees.
27.3 square units
200
In triangle ABC, a = 6, c = 10 and angle B = 76 degrees. Calculate the length of the third side, correct to 2 d.p.
10.34
300
(sec A) / (cot A)
cosec A
300
All solutions 0 to 360 degrees for 2sinA - 1 = 0
30 and 150 degrees
300
In a triangle ABC, a = 10 cm, c = 6 cm and angle C = 30 degrees. Find two possible values of side b, giving the answers to 2 d.p.
5.34 cm and 11.98 cm
300
In a triangle ABC, a = 5 cm, b = 7 cm and angle B = 52 degrees. Find the area of the triangle, correct to 2 d.p.
17.46 sq. cm
300
Two rowers set out from the same point. One rows on a bearing of 070 degrees for 2,000 meters and the other rows on a bearing of 285 degrees for 1,800 meters. How far apart are the two rowers when they stop?
3,625 meters
400
sin A (cosec A - sec A)
1 - tan A
400
All solutions 0 to 360 degrees for 2sinA - √2 = 0
45 and 135 degrees
400
To calculate the height of a building, Reni measures the angle of elevation of the top of the building as 52 degrees. He then walks 20 m closer to the building and measures the angle of elevation as 60 degrees. What is the height of the building, correct to the nearest meter?
98 m
400
The sides of a triangle are 4, 6 and 9 units long. What is the area of the triangle?
9.56 square units
400
A plane takes off at 10:00 from A and flies at 120 km/h on a bearing of 225 degrees. A second plane takes off at 10:05 from A and flies on a bearing of 100 degrees to at 90 km/h. How far apart are the planes at 10:25?
71.6 km
500
cosec A - sin A
(cos²A) / (sin A) or (cos A)(cot A)
500
Solutions 0 to 360 degrees for 2cos² A - 3/2 = 0
30 and 150 and 210 and 330 degrees
500
From a fire tower (A), a fire is spotted on a bearing of 042 degrees. From a second tower (B), the same fire is on a bearing of 348 degrees. It is known that the two towers are 23 km apart and that A is on a bearing of 297 degrees from B. How far, to the nearest kilometre, is the fire from each tower?
22 km from A and 27km from B
500
The four sides of a quadrilateral are 3.5, 4, 5 and 8 meters long, going around in this order. Determine the size of the angle between the 5-meter and 8-meter sides, if the area of the quadrilateral is 22 sq. m. State your answer to the nearest degree.
60 degrees
500
Three circles of radii 5 cm, 6 cm and 8 cm are positioned so that they externally touch one another. Their centre points are connected to form a triangle. What is the size of the largest angle in this triangle? State your answer correct to the nearest degree.
71 degrees