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Law of Sines Worksheet

Law of Sines Worksheet
  • Page 1
 1.  
In ΔABC if A = 35o, b = 15, and c = 28, then find the area of triangle ABC to three significant digits.


a.
420
b.
210
c.
172
d.
120


Solution:

Area of triangle ABC = 12 bc sin A

= 12(15)(28) sin 35o = 120
[Simplify using calculator.]


Correct answer : (4)
 2.  
In ΔABC, if B = 48o, a = 12 and c = 6, then find the area of triangle ABC to two significant digits.


a.
24
b.
27
c.
36
d.
72


Solution:

Area of triangle ABC = 12ac sin B

= 12(12)(6) sin 48o = 27
[Simplify using calculator.]


Correct answer : (2)
 3.  
In ΔPQR, if R = 68o, p = 14 and q = 8, then find the area of triangle PQR to two significant digits.


a.
56
b.
21
c.
42
d.
52


Solution:

Area of triangle PQR = 12 pq sin R

= 12(14)(8) sin 68o = 52


Correct answer : (4)
 4.  
In ΔABC, if A = 54o, B = 62o, and b = 10, then the length of a to two significant digits is:


a.
8.9 units
b.
11 units
c.
9.2 units
d.
10 units


Solution:

Sin 54oa = Sin 62o10
[Using law of sines: sin Aa = sin Bb.]

a = 10 Sin 54oSin 62o

a = 9.2, to two significant digits.


Correct answer : (3)
 5.  
In ΔABC, if A = 62o, b = 12, and a = 20, then what is the measure of the B to the nearest degree?


a.
32o
b.
148o
c.
59o
d.
16o


Solution:

sin 62o20 = sin B12
[Using law of Sines : sin Aa = sin Bb .]

sin B = 12 sin 62o20

sin B = 0.529768555...
[Simplify using calculator.]

B = 32o (or) B = 148o

The measure of 148o is not possible.
[Since 148o + 62o = 210o and 210o is greater than 180o.]

So, B = 32o.


Correct answer : (1)
 6.  
In ΔDEF, if F = 80o, f = 12, e = 26, then the measure of angle E to the nearest degree is:

a.
27o
b.
63o
c.
80o
d.
Cannot be determined


Solution:

sin E26 = sin 80o12
[Using law of sines: sin Ee = sin Ff .]

sin E = 26 sin 80o12

sin E = 2.133750132
[Simplify using calculator.]

This is not possible, because the sine of an angle can be no greater than one.

Therefore, a triangle with the given measurements is not possible.


Correct answer : (4)
 7.  
In ΔDEF, if D = 43.4o, d = 10.8 cm and e = 6.4 cm, then what is the area of the triangle to three significant digits?


a.
34.56 cm2
b.
31.9 cm2
c.
27.05 cm2
d.
12.16 cm2


Solution:

sin 43.4o10.8 = sin E6.4
[Using law of sines: sin Dd = sin Ee .]

sin E = 6.4 sin 43.4o10.8

sin E = 0.407162969

E = 24o

F = 180o - (24o + 43.4o) = 112.6o

Area of triangle DEF = 12 de sin F

= 12(10.8)(6.4) sin 112.6o
[Simplify using calculator.]

= 31.9 cm2


Correct answer : (2)
 8.  
In ΔABC, if E = 34o20', D = 68o30' and f = 16.5 in., then the length of d to three significant digits is:
a.
16.5 units
b.
15.2 units
c.
17.3 units
d.
15.7 units


Solution:


F = 180o - (34o20' + 68o30')

F = 77o10'
[Sum of angle measures in a triangle is 180o.]

sin 77o10′16.5 = sin 68o30′d
[Use the law of sines: sin Ff = sin Dd.]

d = 16.5 sin 68o30′sin 77o10′

d = 15.7 units
[Simplify using calculator.]


Correct answer : (4)
 9.  
In ΔABC, if B = 58o24', b = 23.6 cm and a = 8.2 cm, then the measure of the angle A to the nearest tenth of one degree is:


a.
72.8o
b.
8o24′
c.
60o8′
d.
17.2o


Solution:

sin A8.2 = sin 58o24′23.6
[Use law of sines: sin Aa = sin Bb.]

sin A = 8.2 Sin 58o24′23.6

sin A = 0.295939019
[Simplify using calculator.]

A = 17.2o


Correct answer : (4)
 10.  
In quadrilateral ABCD, if BAD = 90o, AB = 3 units, AD = 4 units, then the length of BC to the nearest two significant digits is:


a.
4.3 units
b.
5 units
c.
3.5 units
d.
5.8 units


Solution:

In Right Triangle BAD, BD2 = BA2 + AD2.

BD2 = 32 + 42 = 25

BD = 5

In Triangle BDC, using law of sines, sin C / BD = sin ∠BDCBC .

sin 60o5 = sin ∠BDCBC

BC = 5sin 48osin 60o

BC = 4.3

The length of BC is 4.3 units.


Correct answer : (1)

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