B. Assume the child is 1.2 meters tall and casts a shadow of 6.4 meters. Determine the angle of the sun at that moment.
what is arctan(1.2/6.4) ?
To determine the angle of the sun at a given moment, we can use trigonometry. The angle of the sun can be found using the concept of similar triangles. Here's how you can find the angle:
1. First, let's label the relevant lengths. The height of the child is 1.2 meters, and the length of the shadow is 6.4 meters.
- Let's denote the height of the child as 'a' and the length of the shadow as 'b'.
2. Now, to find the angle of the sun, we need to consider the tangent ratio (tan) of the angle. The tangent of an angle is the ratio of the opposite side to the adjacent side.
3. In this case, the opposite side is the height of the child (a) and the adjacent side is the length of the shadow (b). So, the tangent of the angle of the sun can be calculated as tan(angle) = a/b.
4. Substituting the given values, we have tan(angle) = 1.2/6.4.
5. Now, we need to find the value of the angle. To do this, we need to take the inverse tangent (arctan) of both sides: angle = arctan(a/b).
6. Plugging in the values, we can calculate the angle using a scientific calculator or a suitable math software: angle = arctan(1.2/6.4).
By following these steps, you should be able to determine the angle of the sun at the moment when the child is 1.2 meters tall and casts a shadow of 6.4 meters.