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Problems
Write complete solutions to the following problems:
1. The length of a rectangle is 5 cm greater than its width. The area is 104 cm2.
Determine the dimensions of the rectangle, to the nearest hundredth of a metre.
2. Bryanna is selling T-shirts. Her regular price is $20 per T-shirt and she usually
sells about 15 T-shirts. Anne finds that, for each reduction in price of $1, she can
sell an additional 2 T-shirts. Determine the maximum revenue and the price at
which this maximum revenue will occur.
3. From the top of a building the angle of elevation of the top of a nearby building is
23 degrees and the angle of depression of the bottom of the nearby building is 52
degrees. The distance between the two buildings is 35 m. What is the height of
the second building? Round your answer to the nearest tenth of a metre.
4. The lengths of two runways at an airport are 1425 m and 875 m and the
beginnings of the runways meet at an angle of 35 degrees, as shown. How far
apart are the ends of the runways, to the nearest metre?
5. Sidra is a passenger in a small aircraft. At the same time, she spots a hydro tower
that is 5.3 km away to the south and a water tower that is 6.5 km away to the
north. The hydro tower and the water tower are separated by a distance of 7.2 km
along the flat ground. Determine the angles at which Sidra is viewing the hydro
tower and the water tower, to the nearest degree.
6. Domenic and Adriana are observing a hot-air balloon from two tracking stations
on the ground. The tracking stations are 6 km apart. From Domenic’s point of
view, the hot-air balloon is at an angle of elevation of 72 degrees. From
Adrianna’s point of view, the angle of elevation is 58 degrees. Determine the
distance that Domenic is from the hot-air balloon, to the nearest tenth of a
kilometre.