Angles of elevation and depression
TrigonometryWe could use a more accurate approach to solve the problem above. We would use trigonometry. The problem above is shown below. We could use; The first step is identifying the known sides. We know the opposite and adjacent. …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. The formula for tangent is; Next we substitute in the values; Then we rearrange to get h on it’s own. Then we work out 100xtan32° on the calculator and round it off to 1d.p. Here we can see that the height of the chimney is 6.25metres.
Angles of depressionJohn is standing on the edge of a cliff. He sees a boat at sea and wonders how far away it is; He is aware that the cliff is 40m high. He measures the angle of depression and finds it is 25°. 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. If the angle of depression is 25° that must mean that angle a is 25° 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. Next we identify the function we need to use from SOHCAHTOA, we can see that; Next we substitute in the known values. The we rearrange the formula to get; If you workout 40÷tan25° on the calculator and round off to 1d.p you get; We have seen that the distance of the boat is 85.8 m
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