Name/ ID:______


Part 1: Angle of elevation 15 marks

Aim: To measure the height of a building at school using trigonometry.

You will need: A clinometer, a trundle wheel, a metre ruler or height chart and a calculator.

Choose a suitable building at school and using a clinometer, apply your trigonometric knowledge to find the height of the building.

  1. Complete the following 7 steps to measure the height of a building.

1 Create a table using the following headings.

Select 5 different suitable distances from the building and carry out the experiment repeating the measurements for each distance.

2 Use the trundle wheel to measure the first distance from the base of the building and stand at that point.

3 Use the clinometer to view and measure the angle of elevation, to the top of the

building. Write this value in the ‘Angle of elevation, column in the table.

4 From the diagram, we can see that: tan θ = h/d, so h = d tan θ . Use this to find h correct to two decimal places and write that value in the ‘Height, h = d tan θ’ column of the table.

5 Measure x, the height of the observer’s eye above the ground, in metres, correct to

two decimal places.

6 Calculate h + x and write the answer in the ‘Revised height, h + x’ column of the

table. This is the height of the building.

7 Repeat this experiment for 4 more values of d, at different distances from the base of the building. Select suitable distances and avoid buildings where construction work is carried on.

  1. Complete the following questions to conclude your report on the height of the building

1. Show the working out that you have done in calculating one of the rows of data in your table.

2. How do your calculated results for the height compare with each other? They are all meant to be the same, but why might the answers be different?

3. How could we come up with a single accurate value for the height of the building,

using these results? Hint: Usually the highest and lowest value for the height of the building are dropped and the average of the three remaining values is considered the most accurate calculation. Explain why this is so.

4. Suggest ways to improve the accuracy of the measurement. Is the percentage error in measurement greater or smaller when closer to the building? Explain why.

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Part 2: Bearings 15 marks

A. Triangular walk:

Leg 1: Starting at point A, walk due East for 3 m to B.

Leg 2: From B, walk due South for 4 m to C.

Q1. How far is C from A? Show working.

Q2. What is the bearing of

  1. A from C?
  2. C from A?

Q3. What is the correct instruction for “Leg 3” if the walk is to end up back at A?

B. Square walk:

Leg 1: Starting at P, walk a bearing of 045 degrees for 8 m to Q.

Leg 2: From Q, walk a bearing of 315 degrees for 8 m to R.

Leg 3: From R, walk a bearing of 225 degrees for 8 m to S.

Q1. Draw a diagram showing the walk.

Q2. How far is S from P?

Q3. What is the bearing of

  1. P from S?
  2. S from P?

Q4. What are the correct instructions for “Leg 4” if the walk is to end up at P?

  1. Your-Own-Shape Walk

Make up your own shape walk modelled upon (but different from) the triangular and square walks above. The walk must have at least 4 “sides” and must finish where it started.

Q1. Describe the walk fully, giving bearings and distances.

Q2. Draw a diagram of the walk.

Q3. Make up a question about the distance between two points on your walk and answer the question showing working.

Q4. Make up a question about bearings (similar to Q3 (i) & (ii) above) between two points on your walk and answer the question.