The manufacturer of a reclining lawn chair would like to have the chair positioned at the following angles: 105,125,145,165 and 175.
B
/ 0 .
/ .
55 / .
/ .
/ .
A/________________.0C
75
Determine the position of the notches(0) on BC that will produce the required angles
To determine the position of the notches on line BC that will produce the required angles, we need to use trigonometry.
Let's assume that the length of line AB is a and BC is b. The length of line AC can be found using the Pythagorean theorem, which states that the square of the hypotenuse (AC) is equal to the sum of the squares of the other two sides (AB and BC).
Using this information, let's solve for the lengths of AC and BD using trigonometry:
1. Angle BAC (angle BAD + angle DAC):
- To find the length of AD, we can use the sine function: sin(angle) = opposite/hypotenuse.
- Since AD is the opposite side and AC is the hypotenuse, we have sin(angle) = AD/AC.
- Solving for AD, we get AD = AC * sin(angle).
2. Angle DAB:
- To find the length of BD, we can use the cosine function: cos(angle) = adjacent/hypotenuse.
- Since BD is the adjacent side and AB is the hypotenuse, we have cos(angle) = BD/AB.
- Solving for BD, we get BD = AB * cos(angle).
Now that we have the lengths of AD and BD in terms of AC and AB, we can calculate their values for each of the given angles (105, 125, 145, 165, and 175).
Keep in mind that we need to know the values of a and b (lengths of AB and BC) to calculate the actual positions of the notches.