Calculating distance II 0 Overview Using this Resource Connecting to the Curriculum Marking Student Responses Working with Students Further Resources This task is about using trigonometry to calculate distances in practical problems. Use the formulae in the box to answer the following questions. Question 2Change answer a) A jet plane climbs at an angle of 60° and travels a distance of 3000 metres. [Not drawn to scale] a) A jet plane climbs at an angle of 60° and travels a distance of 3000 metres. [Not drawn to scale] How far has the plane travelled in the horizontal direction, shown by 'w'? metres Question 2Change answer b) A submarine dives at an angle of 40° for 935 metres. [Not drawn to scale] b) A submarine dives at an angle of 40° for 935 metres. [Not drawn to scale] Calculate the depth the submarine will be at after the dive, shown by 'x'. metres Question 2Change answer c) Simon and Maraea are playing golf. Maraea is 110 metres away from the hole. Simon is standing at an angle of 17° from Maraea and the hole. [Not drawn to scale] c) Simon and Maraea are playing golf. Maraea is 110 metres away from the hole. Simon is standing at an angle of 17° from Maraea and the hole. [Not drawn to scale] How far is John from the hole, shown by 'y'? metres Question 2Change answer d) Josh watched a space shuttle launch. When the space shuttle was 15 km above the Earth, there was an angle of 60° between where Josh was standing, the space shuttle, and the launch site. [Not drawn to scale] d) Josh watched a space shuttle launch. When the space shuttle was 15 km above the Earth, there was an angle of 60° between where Josh was standing, the space shuttle, and the launch site. [Not drawn to scale] Calculate how far Josh was from the launch site, shown by 'z'. km Task administration: This task can be completed with pen and paper or online (with NO auto marking). Level: 5 Curriculum info: Maths, Geometry and Measurement, Shape Keywords: trigonometry, sine, cosine, tangents Description of task: Using given trigonometry ratios, students calculate distances in practical problems. Answers/responses: Y10 (10/1998) a) 1500 moderate b) 601 [Accept 600-601.5] moderate c) 115.03 [Accept 115-115.1] very difficult e) 8.66 [Accept 8.6-8.7] difficult Diagnostic and formative information: Common error Likely calculation Likely reason c) 105 or close 110 cos 17° Wrong manipulation of 110 ÷ y = cos 17°. d) 25.9, 26, 25 or close13 15 tan 60°15 tan 60° ÷ 2 Wrong manipulation of 15 ÷ z = tan 60°.As above but halves answer to make it look plausible. Calculating distance III Distance between people Using trigonometry to calculate length Calculating distance Tracking sports professionals Kicking for goal Calculating lengths and heights Sails for the yacht
