Angles of elevation and depression


This chapter explores angles of elevation and depression. It covers working with angles of elevation and depression and using scale drawing and trigonometry to calculate heights of tall objects. No prior knowledge is required for this chapter. Engineers use trigonometry to work out very high heights such as a tree and tall buildings. The following image shows an old chimney. Engineers need to work out how tall it is; Angles of elevation and depression The engineers stand 100m from the chimney. They measure the angle of elevation shown below using a theodolite. Angles of elevation and depression2 They find out that the angle of elevation is 32°. Suppose they wanted to work out the height. Angles of elevation and depression3 One way to work out the height of the chimney is to so a scale drawing. We could use a scale of 1cm for 10m. First we draw a line 10cm long. Angles of elevation and depression4 Then we draw an angle of 32 ° as shown below. Angles of elevation and depression5 Then we join the height. Angles of elevation and depression6 Finally we measured the height using a ruler. You’ll find that it is 6.3cm. Angles of elevation and depression7 6.3cm represents 63metres in the scaling above. We have found out that the chimney is 63m high.

Trigonometry

We could use a more accurate approach to solve the problem above. We would use trigonometry. The problem above is shown below. Angles of elevation and depression8 We could use; Angles of elevation and depression9 The first step is identifying the known sides. We know the opposite and adjacent. Angles of elevation and depression10 ...h is the opposite and 100 is the adjacent. The second step is identifying the tangent function that we need to use. Using SOHCAHTOA we can use that we need to use tangent. Angles of elevation and depression11 The formula for tangent is; Angles of elevation and depression12 Next we substitute in the values; Angles of elevation and depression13 Then we rearrange to get h on it’s own. Angles of elevation and depression14 Then we work out 100xtan32° on the calculator and round it off to 1d.p. Angles of elevation and depression15 Here we can see that the height of the chimney is 6.25metres.

Angles of depression

John is standing on the edge of a cliff. He sees a boat at sea and wonders how far away it is; Angles of elevation and depression16 He is aware that the cliff is 40m high. Angles of elevation and depression17 He measures the angle of depression and finds it is 25°. Angles of elevation and depression18 Suppose he wanted to find the distance to the boat. Below is a diagram which we can form from the problem to help solve it. Angles of elevation and depression19 If the angle of depression is 25° that must mean that angle a is 25° Angles of elevation and depression20 Now we don’t need the angle of depression since the inner angle is known. We would use SOHCAHTOA to solve the problem. First we identify the sides we know. We have the opposite and adjacent. Angles of elevation and depression21 Next we identify the function we need to use from SOHCAHTOA, we can see that; Angles of elevation and depression22 Next we substitute in the known values. Angles of elevation and depression23 The we rearrange the formula to get; Angles of elevation and depression24 If you workout 40÷tan25° on the calculator and round off to 1d.p you get; Angles of elevation and depression25 We have seen that the distance of the boat is 85.8 m ;
//Comments This chapter explores angles of elevation and depression. It covers working with angles of elevation and depression and using scale drawing and trigonometry to calculate heights of tall objects. No prior knowledge is required for this chapter. Engineers use trigonometry to work out very high heights such as a tree and tall buildings. The following image shows an old chimney. Engineers need to work out how tall it is; Angles of elevation and depression The engineers stand 100m from the chimney. They measure the angle of elevation shown below using a theodolite. Angles of elevation and depression2 They find out that the angle of elevation is 32°. Suppose they wanted to work out the height. Angles of elevation and depression3 One way to work out the height of the chimney is to so a scale drawing. We could use a scale of 1cm for 10m. First we draw a line 10cm long. Angles of elevation and depression4 Then we draw an angle of 32 ° as shown below. Angles of elevation and depression5 Then we join the height. Angles of elevation and depression6 Finally we measured the height using a ruler. You’ll find that it is 6.3cm. Angles of elevation and depression7 6.3cm represents 63metres in the scaling above. We have found out that the chimney is 63m high.

Trigonometry

We could use a more accurate approach to solve the problem above. We would use trigonometry. The problem above is shown below. Angles of elevation and depression8 We could use; Angles of elevation and depression9 The first step is identifying the known sides. We know the opposite and adjacent. Angles of elevation and depression10 ...h is the opposite and 100 is the adjacent. The second step is identifying the tangent function that we need to use. Using SOHCAHTOA we can use that we need to use tangent. Angles of elevation and depression11 The formula for tangent is; Angles of elevation and depression12 Next we substitute in the values; Angles of elevation and depression13 Then we rearrange to get h on it’s own. Angles of elevation and depression14 Then we work out 100xtan32° on the calculator and round it off to 1d.p. Angles of elevation and depression15 Here we can see that the height of the chimney is 6.25metres.

Angles of depression

John is standing on the edge of a cliff. He sees a boat at sea and wonders how far away it is; Angles of elevation and depression16 He is aware that the cliff is 40m high. Angles of elevation and depression17 He measures the angle of depression and finds it is 25°. Angles of elevation and depression18 Suppose he wanted to find the distance to the boat. Below is a diagram which we can form from the problem to help solve it. Angles of elevation and depression19 If the angle of depression is 25° that must mean that angle a is 25° Angles of elevation and depression20 Now we don’t need the angle of depression since the inner angle is known. We would use SOHCAHTOA to solve the problem. First we identify the sides we know. We have the opposite and adjacent. Angles of elevation and depression21 Next we identify the function we need to use from SOHCAHTOA, we can see that; Angles of elevation and depression22 Next we substitute in the known values. Angles of elevation and depression23 The we rearrange the formula to get; Angles of elevation and depression24 If you workout 40÷tan25° on the calculator and round off to 1d.p you get; Angles of elevation and depression25 We have seen that the distance of the boat is 85.8 m ;
© 2015 All rights reserved.