• 25 metres

• 28.87 metres

• 43.30 metres

• 50 metres

Answer explanation

Using the tangent function: height = distance * tan(angle). Here, height = 50 * tan(30°) = 50 * (1/√3) ≈ 28.87 metres. Thus, the height of the building is approximately 28.87 metres.

• Sine Law

• Cosine Law

• Pythagorean Theorem

• None of the above

Answer explanation

The Sine Law is appropriate here because we have two sides and the angle opposite one of them. It allows us to find the unknown angle opposite side b using the known angle and the sides.

• Sine Law

• Cosine Law

• Pythagorean Theorem

• None of the above

Answer explanation

To find the angle opposite side c in a triangle with known sides, the Cosine Law is appropriate. It relates the lengths of the sides to the cosine of one angle, making it suitable for this scenario.

• 3 metres

• 5 metres

• 6 metres

• 9 metres

Answer explanation

Using the cosine function: cos(60°) = adjacent/hypotenuse. Here, adjacent = 3m (distance from wall), so hypotenuse (ladder length) = 3m/cos(60°) = 3m/(1/2) = 6m. Thus, the ladder is 6 metres long.

• 5.14 cm

• 6.01 cm

• 10.39 cm

• 11.54 cm

Answer explanation

Using the Law of Cosines: c² = a² + b² - 2ab * cos(C). Plugging in values: c² = 10² + 12² - 2*10*12*cos(30°). This simplifies to c² = 100 + 144 - 120*√3/2. Calculating gives c ≈ 6.01 cm, the correct answer.

• 68.40 km

• 70.71 km

• 73.20 km

• 76.60 km

Answer explanation

To find the altitude of point B, use the formula: altitude = distance * sin(angle). Here, altitude = 200 km * sin(20°) ≈ 68.40 km. Thus, the correct answer is 68.40 km.

• Sine Law

• Cosine Law

• Pythagorean Theorem

• None of the above

Answer explanation

To find the angle opposite side a in a triangle with sides a, b, and c, the Cosine Law is appropriate. It relates the lengths of the sides to the cosine of one of the angles, making it suitable for this scenario.

• 8.50 cm

• 10.61 cm

• 11.31 cm

• 13.42 cm

Answer explanation

Using the Law of Cosines: c² = a² + b² - 2ab * cos(C). Plugging in values: c² = 9² + 12² - 2*9*12*cos(45°). This simplifies to c² = 81 + 144 - 108√2. Calculating gives c ≈ 8.50 cm.

A ship sails 100 km east and then 150 km north. What is the straight-line distance from the starting point to the final position of the ship?

• 150 km

• 180 km

• 200 km

• 250 km

Answer explanation

To find the straight-line distance, use the Pythagorean theorem: distance = √(100² + 150²) = √(10000 + 22500) = √32500 = 180 km. Thus, the correct answer is 180 km.

• 7.21 cm

• 8.66 cm

• 9.54 cm

• 10.39 cm

Answer explanation

Using the Law of Cosines: c² = a² + b² - 2ab * cos(C). Plugging in the values: c² = 6² + 8² - 2*6*8*cos(60°) = 36 + 64 - 48 = 52. Thus, c = √52 ≈ 7.21 cm, which is the correct answer.