the side of a tent makes an angle of 65 to the ground. if a boy who is 1.1m tall stands inside the tent with his head touching the tent's peak, how long is the fabric that makes up the side of the tent
r = 1.1/sin65 = 1.21 m.
To find the length of the fabric that makes up the side of the tent, we can use the concept of trigonometry. In this case, we can use the tangent of the angle to determine the relationship between the height of the tent and the length of the fabric.
Here's the step-by-step solution:
1. Draw a diagram of the scenario. Label the angle between the side of the tent and the ground as 65 degrees (°) and the height of the boy inside the tent as 1.1 meters (m).
2. Identify the side of the right-angled triangle that represents the length of the fabric. In this case, it is the side opposite to the angle we are given.
3. Use the tangent function to find the length of the fabric. Tangent is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.
tangent(angle) = Opposite / Adjacent
In this case, the angle is 65° and the opposite side is the length of the fabric we want to find. The adjacent side is the height of the boy, which is 1.1m.
Therefore, we have:
tan(65°) = Length of fabric / 1.1m
4. Solve for the length of the fabric.
Rearranging the equation, we get:
Length of fabric = tan(65°) * 1.1m
Using a scientific calculator, find the tangent of 65°, and then multiply it by 1.1m to find the length of the fabric.
So, using trigonometry, the length of the fabric that makes up the side of the tent can be determined.