1) How tall is an object if an observer views the top of the object at an angle of elevation of \(23\) degrees, standing \(32\) feet away from the object? Round your answer to the nearest two decimal places.
2) How far from an object is an observer standing if his angle of depression to the bottom of the object is \(12.2^{\circ}\) and the size of the object is \(14\) meters? Round your answer to the nearest two decimal places.
4) Suppose you have to look down at a \(10^{\circ}\) degree angle to see the top of your niece, Missy’s, head. If you are \(6’ 1”\)and standing \(15\) feet away from her, how tall is Missy? Round her height to the nearest tenth of a foot.
5) At the top of a lighthouse \(28\) m above sea level a spotter sees a boat in the distance at an angle of depression of \(16.4^{\circ}\). How far is the boat from shore (the base of the lighthouse).
5) At the top of a lighthouse \(28\) m above sea level a spotter sees a boat in the distance at an angle of depression of \(16.4^{\circ}\). How far is the boat from shore (the base of the lighthouse).
6) A fire tower at the top of cliff overlooks a large valley. Fire fighters often use these towers to spot potential fires. Suppose the top of this tower averages \(112\) meters above the valley floor and fire spotter sees smoke at a \(12.2^{\circ}\) angle of depression from his line of sight. How far away is the fire from the bottom of the cliff?
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8) A woman is standing a certain distance from a building. She knows that the building is \(250\) feet high and she measures the angle of elevation to be \(25^{\circ}\). How far is she from the base of the building if her eye level is at \(5'1"\)?
9) A surveyor wishes to know the height of a certain building. At a distance of \(100\) feet from the building (on level ground), he measures the angle of elevation to the top of the building to be \(72.5^{\circ}\). How tall is the building?
9) A surveyor wishes to know the height of a certain building. At a distance of \(100\) feet from the building (on level ground), he measures the angle of elevation to the top of the building to be \(72.5^{\circ}\). How tall is the building?
10) A person is standing at the top of a cliff \(1000\) feet high at the edge of the ocean. At a certain time, she sights a boat in the water at an angle of depression of \(23^{\circ}\). A moment later she sights the same boat at an angle of depression of \(31^{\circ}\). How far has the boat traveled between the two sightings?
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11) A flagpole stands atop a \(65\) ft. building. From a position, an observer whose eyes are \(5\) ft. above the ground, the angles of elevation of the top and bottom of the flagpole are \(47^{\circ}\) and \(41^{\circ}\), respectively. Find the length of the flagpole.
12) The tower bridge (London England Thames Tower Bridge) has a central span of \(200\) feet between two towers which can be split evenly into two leaves and lifted to a maximum angle of \(86^{\circ}\) to allow taller river traffic to pass. If the original height of the leaves is \(28\) feet above the water, what clearance does the bridge allow when raised? That is, what is the highest point on the original bridge above the water?
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13) The Petronas Towers, also known as the Petronas Twin Towers are in Malaysia. They are the tallest twin towers in the world. The towers feature a skybridge connecting the two towers on the \(41\)st floor that is \(58.4\) meters long. Suppose you just enter the skybridge and looking up at an angle of \(76.4^{\circ}\) you can see the top of the adjoining tower and looking down at an angle of \(74.5^{\circ}\) you can see the bottom of the same adjoining tower. How tall are the buildings?
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14) The soldier is on a swing whose chain is \(6.25\) feet long and \(23\) inches off the ground when not moving. How high off the ground is this soldier whose swing is at \(85^{\circ}\) as shown?