1.
Solve this right triangle. Give the measures to the nearest tenth.
Solution: UW = √(13²+6.5²)≈14.5 cm. tan(∠W)=6.5/13, so ∠W≈26.6° and ∠U≈63.4°.
2.
Ann and Byron positioned themselves 35 m apart on one side of a stream. Ann measured the angles as shown below. Calculate the height of the cliff on the other side of the stream.
Solution: cos(36°)=35/y, so y≈43.26 m. Then tan(68°)=x/43.26, so x≈107.1 m.
3.
Solve this right triangle. Give the measures to the nearest tenth.
Solution: ∠F = 90° - 23° = 67°. sin(23°)=8/FH, so FH≈20.5 m. Then GH≈18.8 m.
4.
A water taxi leaves its dock, and travels 7 km due north to pick up medical supplies. It then travels 15 km due east to drop off the supplies at a hospital. To the nearest degree, what is the measure of the angle between the path it took due east and the path it will take to return directly to its dock?
Solution: tan(x)=7/15≈0.467. Therefore x≈25°.
5.
Determine the perimeter of this rhombus to the nearest tenth of a centimetre.
Solution: sin(64°)=3.7/x, so x≈4.12 cm. Perimeter = 4(4.12)≈16.5 cm.
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