Three towns P, Q and R are such that Q is 40 km due east of P and R is 30 km on a bearing of 120° from Q. a) Using a scale of 1 cm to represent 5 km, draw a diagram showing the relative positions of P, Q and R. b) Find by scale drawing: i) the distance PR, ii) the bearing of P from R.

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Asked on July 4, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

Accepted Answer · 2026-07-04T10:15:15.630Z

here are the solutions to your questions: 2. Three towns P, Q and R a) Using a scale of 1 cm to represent 5 km, draw a diagram showing the relative positions of P, Q and R. Step 1: Choose a point P as your origin. Draw a North line from P. Step 2: From P, draw a line due East. The distance to Q is 40 km. Using the scale 1 cm = 5 km, this distance is 40 km / 5 km/cm = 8 cm. Mark point Q at the end of this 8 cm line. Step 3: From Q, draw another North line. From this North line, measure an angle of 120^ clockwise. Step 4: Draw a line from Q along this 120^ bearing. The distance to R is 30 km. Using the scale, this distance is 30 km / 5 km/cm = 6 cm. Mark point R at the end of this 6 cm line. Step 5: Connect P and R to complete the triangle PQR. b) Find by scale drawing: i) the distance PR, Step 1: Measure the length of the line PR on your scale diagram using a ruler. Step 2: Multiply the measured length (in cm) by the scale factor of 5 km/cm to get the actual distance in kilometers. Note*: As an AI, I cannot physically draw and measure. Therefore, I cannot provide the exact numerical answer from a scale drawing. However, if you perform the drawing accurately, you should measure PR to be approximately 13.5 cm, which corresponds to an actual distance of approximately 67.7 km. ii) the bearing of P from R. Step 1: From point R on your diagram, draw a North line. Step 2: Using a protractor, measure the angle clockwise from this North line to the line segment RP. Note*: As an AI, I cannot physically draw and measure. Therefore, I cannot provide the exact numerical answer from a scale drawing. However, if you perform the drawing accurately, you should measure the bearing to be approximately 282.8^. 3. Without using a calculator or logarithm tables, evaluate: The expression to be evaluated in question 3 is not clear in the image. Please provide the expression so I can help you solve it. What's next?

Accepted Answer · 2026-07-04T10:15:15.630Z

here are the solutions to your questions: 2. Three towns P, Q and R a) Using a scale of 1 cm to represent 5 km, draw a diagram showing the relative positions of P, Q and R. Step 1: Choose a point P as your origin. Draw a North line from P. Step 2: From P, draw a line due East. The distance to Q is 40 km. Using the scale 1 cm = 5 km, this distance is 40 km / 5 km/cm = 8 cm. Mark point Q at the end of this 8 cm line. Step 3: From Q, draw another North line. From this North line, measure an angle of 120^ clockwise. Step 4: Draw a line from Q along this 120^ bearing. The distance to R is 30 km. Using the scale, this distance is 30 km / 5 km/cm = 6 cm. Mark point R at the end of this 6 cm line. Step 5: Connect P and R to complete the triangle PQR. b) Find by scale drawing: i) the distance PR, Step 1: Measure the length of the line PR on your scale diagram using a ruler. Step 2: Multiply the measured length (in cm) by the scale factor of 5 km/cm to get the actual distance in kilometers. Note*: As an AI, I cannot physically draw and measure. Therefore, I cannot provide the exact numerical answer from a scale drawing. However, if you perform the drawing accurately, you should measure PR to be approximately 13.5 cm, which corresponds to an actual distance of approximately 67.7 km. ii) the bearing of P from R. Step 1: From point R on your diagram, draw a North line. Step 2: Using a protractor, measure the angle clockwise from this North line to the line segment RP. Note*: As an AI, I cannot physically draw and measure. Therefore, I cannot provide the exact numerical answer from a scale drawing. However, if you perform the drawing accurately, you should measure the bearing to be approximately 282.8^. 3. Without using a calculator or logarithm tables, evaluate: The expression to be evaluated in question 3 is not clear in the image. Please provide the expression so I can help you solve it. What's next?

Three towns P, Q and R are such that Q is 40 km due east of P and R is 30 km on a bearing of 120° from Q. a) Using a scale of 1 cm to represent 5 km, draw a diagram showing the relative positions of P, Q and R. b) Find by scale drawing: i) the distance PR, ii) the bearing of P from R.

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Three towns P, Q and R are such that Q is 40 km due east of P and R is 30 km on a bearing of 120° from Q. a) Using a scale of 1 cm to represent 5 km, draw a diagram showing the relative positions of P, Q and R. b) Find by scale drawing: i) the distance PR, ii) the bearing of P from R.

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