1) In each problem use inverse trigonometry to find the measure of theta (\(\theta\)). Make sure you label the sides “opposite”, “adjacent” and “hypotenuse” to the respective angle. After finding \(\theta\), use complementary angles to find the measure of the third angle.
2) ADA Ramp Specifications require a \(1:12\) wheelchair ramp slope ratio. That is, for every \(1\) unit of rise there must be \(12\) units of run. What is the angle of elevation for this specification?
5) This is a picture of the suspension bridge called the Millou Viaduct in Millou, France. The bridge was designed by Norman Foster. The pillars are \(285\) feet high.
a) The highest cable is attached at \(262\) feet above the bridge and is attached \(162\) feet on the bridge away from the pillar. Find the angle between the highest cable and the pillar.
b) The lowest cable is attached \(211\) feet above the bridge and is attached \(34\) feet on the bridge away from the pillar. Find the angle between the lowest cable and the pillar.
a) The highest cable is attached at \(262\) feet above the bridge and is attached \(162\) feet on the bridge away from the pillar. Find the angle between the highest cable and the pillar.
b) The lowest cable is attached \(211\) feet above the bridge and is attached \(34\) feet on the bridge away from the pillar. Find the angle between the lowest cable and the pillar.
6) Solve each triangle. That is, find the missing side and both missing angles in each triangle.
8) In this game, a player released a ring on a swing attempting to catch a hook which is hanging on a wall. If the hook is \(5\) feet off the ground, the ceiling height is \(8\) feet, and the string is tethered \(5\) feet, \(9\) inches from the wall, at what angle should the player release the hook?
10) You just bought a satellite dish for a new television network. Your neighbor helps you install it so that the dish properly receives its signal. The bottom of the dish must be placed \(5.2\) inches from the wall and the dish itself is \(19.3\) inches long. The top of the dish will lean against the wall. At what angle is the dish facing the southern sky?
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11) \(\triangle ABC\) is reflected in the \(y = -1\) line and then translated by the rule \((x, y) → (x + 4, y)\). What is the \(m\angle F\)?