Precalculus
Wkst- Law of Sines/Area of a Triangle
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Law of Sines
For #1-4, solve the triangle using the Law of Sines (find all missing angles and sides).
1) A = 60°
B = 76°
c = 10
2) B = 40°
C = 105°
3) A = 24.3°
C = 54.6°
4) C = 145°
b=4
c = 20
c = 2.68
c = 14
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5) A satellite orbiting the earth passes directly overhead at observation stations in Phoenix and Los Angeles,
340 mi. apart. At an instant when the satellite is between these two stations, its angle of elevation is
simultaneously observed to be 60 at Phoenix and 75 at Los Angeles. How far is the satellite from Los
Angeles?
6) The longer diagonal of a parallelogram makes angles of 29 and 56 with its sides, and its length is 23 in.
Find the length of the longer side of the parallelogram.
7) To measure the height of the Eiffel Tower in Paris, a person stands away from the base and measures the
angle of elevation to the top of the tower to be 60o. Moving 210 feet closer, the angle of elevation to the top of
the tower is 70o . How tall is the Eiffel Tower?
8) To find the distance from the house at A to the house at B, a surveyor measures the angle BAC to be 40
and then walks off a distance of 100 feet to C and measures angle ACB to be 58 . What is the distance from A
to B?
9) A pilot is flying over a straight highway. He determines the angles of depression to two mileposts, 5 miles
apart, to be 32 and 48 . Find the distance of the plane from ends of the highway.
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10) Points A and B are separated by a lake. To find the distance between them, a surveyor locates a point C on
land such that angle CAB = 48.6 . He also measures CA as 312 ft. and CB as 527ft. Find the distance between
A and B.
11) The longer diagonal of a parallelogram makes angles of 38 and 44 with the sides, and its length is 15 in.
Find the length of the shorter side of the parallelogram.
12) A parcel of land is in the shape of an isosceles triangle. The base has length 425 feet; the other sides, which
are of equal length, meet at an angle of 39 . How long are they?
13) Because of prevailing winds, a tree grew so that it
was leaning 4° from the vertical. At a point 35 meters
from the tree, the angle of elevation to the top of the
tree is 23 . Find the height of the tree.
14) In traveling across flat land, you notice a
mountain directly in front of you. Its angle of
elevation (to the peak) is 3.5°. After you drive 13
miles closer to the mountain, the angle of elevation is
9°. Approximate the height of the mountain.
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Area of a triangle
1) Given: a = 3, b = 4, C = 40°. Find the area
of the triangle.
2) The adjacent sides of a parallelogram are 18
and 26 cm long, and one angle measures 70°.
Find the area of the parallelogram.
3) A triangular parcel of land has sides
measuring 25 yards, 31 yards, and 50 yards.
What is the area of the land?
4) Find the area of the regular pentagon which is
inscribed in a circle with radius 8.7 ft.
5) Find the area of a triangular parcel of land if two adjacent sides have measures of 14 and 27 yards, and
the angle in between measures 150°.
6) The lengths of the sides of a triangular parcel of land are 200 feet, 500 feet and 600 feet. Find the area of
the parcel.
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7) You want to buy a triangular lot measuring 510 yards by 840 yards by 1120 yards. The price of the land
is $2000 per acre. How much does the land cost? (Hint: 1 acre = 4840 square yards)
8) A parking lot has the shape of a parallelogram (see figure). The lengths of two adjacent sides are 70
meters and 100 meters. The angle between the two sides is 70°. What is the area of the parking lot?
9) Find the area of a regular nonagon (9 sides) inscribed in a circle of radius 10 in.
10) Find the area of a regular hexagon inscribed in a circle of radius of 12 in.
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