# Harvard University Laws of Sines and Cosines Questions

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MTH 112 FWH 7 – Solving Triangles with Laws of Sines and Cosines
1. Solve each triangle for the unknown sides and angles using the Laws of Sines and Cosines as
appropriate. If there is more than one possible solution, give both. If it is not possible, so
state. Let side a be across from angle α, side b be across from angle β and side c be across
from angle γ.
a. α = 75◦ , a = 25, b = 40
d. γ = 110◦ , b = 5, c = 15
b. β = 62◦ , a = 11, b = 13
e. α = 40◦ , a = 180, b = 232.6
c. α = 145◦ , b = 25, c = 42
f. β = 61◦ , a = 12.1, c = 16.3
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2. A 113 foot tower is located on a hill that is inclined 24◦ to the horizontal. A guy-wire is to be
attached to the top of the tower and anchored at a point 55 feet uphill from the base of the
tower. Find the length of wire needed.
3. To estimate the height of a building, two students find the angle of elevation from a point (at
ground level) down the street from the building to the top of the building is 12◦ . From a
point that is 250 feet closer to the building, the angle of elevation (at ground level) to the top
of the building is 20◦ . If we assume that the street is level, use this information to estimate
the height of the building.
4. Two planes leave the same airport at the same time. One flies at 35◦ west of north at 450
miles per hour. The second flies at 30◦ south of west at 380 miles per hour. How far apart
are the planes after 2 hours?
5. The four sequential sides of a quadrilateral have lengths 5.7 cm, 7.2 cm, 9.4 cm, and 12.8 cm.
The angle between the two smallest sides is 106◦ . What is the area of this quadrilateral?
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Solving Triangles

Laws of Sines and Cosines

Laws of Sines

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