The bearing of a town p from another town q is 75°. What is the bearing of q from p
2. Ibadan is on a bearing of 240°from yola. What is the bearing from yola to ibadan.
3. From the top of a building 10m high the angle of depression of a stone lying on the horizontal ground is 60°. Calculate the difference of the stone from the foot of the building
Answer
1. To determine the bearing of q from p, we need to find the opposite direction of the bearing from p to q. Since the bearing from p to q is 75°, the opposite direction would be 180° + 75° = 255°. Therefore, the bearing of q from p is 255°.
2. To find the bearing from yola to ibadan, we need to subtract the bearing from ibadan to yola from 360°. The bearing from ibadan to yola is 240°, so we have 360° - 240° = 120°. Therefore, the bearing from yola to ibadan is 120°.
3. From the top of the building, the angle of depression of the stone lying on the horizontal ground is 60°. This means that the angle between the line of sight from the top of the building to the stone and the horizontal ground is 60°.
Since the line of sight from the top of the building to the stone forms a right triangle with the height of the building as the opposite side and the distance from the foot of the building to the stone as the adjacent side, we can use trigonometry to find the difference.
We can use the tangent function, which is defined as the opposite side divided by the adjacent side. In this case, the tangent of the angle of depression is equal to the height of the building divided by the difference. Therefore, we have:
tan(60°) = 10m / difference
Simplifying, we have:
√3 = 10m / difference
To isolate the difference, we can multiply both sides by difference:
√3 * difference = 10m
Dividing both sides by √3, we have:
difference = 10m / √3
Calculating this, we get:
difference ≈ 5.77m
Therefore, the difference between the stone and the foot of the building is approximately 5.77m.
To find the bearing of one point from another, you need to subtract the bearing of the first point from 180°. The result will give you the bearing from the second point to the first point.
1. Bearing of P from Q is 75°. To find the bearing of Q from P, we subtract 75° from 180°.
Bearing of Q from P = 180° - 75° = 105°
Therefore, the bearing of Q from P is 105°.
2. Ibadan is on a bearing of 240° from Yola. To find the bearing from Yola to Ibadan, we need to add 180° to the given bearing.
Bearing from Yola to Ibadan = 240° + 180° = 420°
Therefore, the bearing from Yola to Ibadan is 420°.
3. From the top of a building 10m high, the angle of depression of a stone on the horizontal ground is 60°. To calculate the difference between the stone and the foot of the building, we can use trigonometry.
Let x be the distance between the foot of the building and the stone.
Using the tangent function, we have:
tan(60°) = 10m / x
To solve for x, we can rearrange the equation:
x = 10m / tan(60°)
Using a calculator, we find:
x = 10m / 1.732
x ≈ 5.77m
Therefore, the difference between the stone and the foot of the building is approximately 5.77m.