Question

1. fireworks the designers of a fireworks display want to have four fireworks travel along parallel trajectories. they decide to place two launchers on a dock and two launchers on the roof of a building. to make this display work correctly, what should the measure of angle 1 be? explain.
2. analyze problems chaska is making a giant letter a to put on the rooftop of the a is for apple orchard store. the figure shows a sketch of the design.

a. what should the measures of angles 1 and 2 be so the horizontal part of the a is truly horizontal? explain.
b. when building the a, chaska makes sure that angle 1 is correct, but when he measures angle 2, it is not correct. what does this imply about the a?

Explanation:

Step1: Use the property of supplementary angles

For part a, since the horizontal part is truly horizontal, the sum of angle 2 and \(108^{\circ}\) is \(180^{\circ}\) (supplementary angles). So, \(\angle2 = 180^{\circ}- 108^{\circ}\).
$$\angle2=72^{\circ}$$
Because of the symmetry of the letter “A” (assuming the two non - horizontal sides are symmetric with respect to the vertical line through the middle of the horizontal part), \(\angle1=\angle2\).

Step2: Analyze the implication for part b

For part b, if \(\angle1\) is correct (\(\angle1 = 72^{\circ}\)) and \(\angle2
eq72^{\circ}\), then the horizontal part of the “A” is not truly horizontal. This is because for the horizontal part to be horizontal, the angles on either side ( \(\angle1\) and \(\angle2\)) should be equal (due to the symmetry required for the horizontal alignment with respect to the two non - horizontal sides of the “A” - shaped structure)

Answer:

a. \(\angle1 = 72^{\circ}\), \(\angle2 = 72^{\circ}\). Because \(\angle2\) and \(108^{\circ}\) are supplementary (\(\angle2=180 - 108=72^{\circ}\)), and by symmetry \(\angle1=\angle2\).
b. The horizontal part of the “A” is not truly horizontal.