With test

1) if possible, find the area of the triangle defined by the following: b = 45, c = 20, a = 71.

a) 405.2 square units
b) 425.5 square units
c) 189.1 square units
d) 465.4 square units

solve the triangle: b=12, c=10 b=45 . if it is not possible, say so.

a) a=77, a=15.6, y=58
b) this triangle is not solvable
c) a=98.9, a=16.8, y=36.1
d) a=58, a=13.8, y=77

3)
a street light is mounted on a pole. the tip of the shadow of a man who is standing on a street a short distance from the pole has an angle of elevation to the top of his head of 28°. a woman standing in the opposite direction of the pole as the man was standing on the same street has a angle of elevation from the tip of her shadow to her head of 24°. if the two people are 20 feet apart, how far is the street light from the head of the woman?

a) the street light is 9.1 feet from the head of the woman.
b)the street light is 10.9 feet from the head of the woman.
c)the street light is 11.9 feet from the head of the woman.
d) the street light is 10.3 feet from the head of the woman.

4) solve the triangle: a = 7, b = 9, c = 100°. if it is not possible, say so.

a) a=40, b=40, c=11
b) this triangle is not solvable
c) a=46, b=34, c=11.4
d) a=34, b=46, c=12.3

the triangle described is of the form ssa. determine if there is no triangle possible, one triangle possible, or two triangles possible. if only one triangle is possible, solve the triangle. if either two triangles may be formed or no triangle may be formed, say so. the triangle is defined by: a=10, b=12, b=45

a)a=36.1, y=98.9, c=16.8
b) a=98.9, y=36.1, c=16.8
c)no triangle can be formed from this information.
d) two triangles may be formed.

solve the triangle: a = 8, b = 10, c = 3. if it is not possible, say so.

a) this triangle is not solvable
b) a=41.4, b=124.2, c=14.4
c) a=124.4, b=14.4, c=41.4
d) a=14.4, b=41.4, c=124.2

if possible, find the area of the triangle defined by the following: b = 11, c = 8, a = 28°.

a) 44 square units
b) 20.7 square units
c) 21.8 square units
d) 74.8 square units

for the function given, state the starting point for a sample period: ƒ(t) = 0.2sin (t − 0.3) + 0.1.

a) (0.3, 0)
b) (0.3, 0.2)
c) (0.3, 0.1)
d) (0.3, 1)

the triangle described is of the form ssa. determine if there is no triangle possible, one triangle possible, or two triangles possible. if only one triangle is possible, solve the triangle. if either two triangles may be formed or no triangle may be formed, say so. the triangle is defined by: a=10, c=8, y=30

a) two triangles may be formed
b) a=38.6 b=111.4, b=14.9
c) no triangle can be formed from this information
d) a=141.3, b=8.7, b=2.4

Part 1) the correct question is
If possible, find the area of the triangle defined by the following: b = 45, c = 20, A = 71°
The area of the triangle will be given by:
Area=1/2b*c sin A
Area=1/2*45*20*sin 71
Area=425.48 units²> 425.5 units²
=425.5 square units

The answer Part 1) is  425.5 square units


Part 2)Solve the triangle: b=12, c=10 B=45 . If it is not possible, say so.

applying the law of sines
b/sin B=c/sin C> b*sin C=c*sin B> sin C=(c/b)*sin B
sin C=(10/12)*sin 45> sin C=0.5892
C=arc sin(05892)> C=36.1°
A=180-(45+36.1)> A=98.9°
b/sin B=a/sin A> a=b*sin A/sin B> a=12*sin 98.9/sin 45
a=16.77> a=16.8

a=16.8 b=12  c=10
A=98.9° B=45° C=36.1°

the answer is the option
C) a=98.9, a=16.8, y=36.1

Part 3) A street light is mounted on a pole. The tip of the shadow of a man who is standing on a street a short distance from the pole has an angle of elevation to the top of his head of 28°. A woman standing in the opposite direction of the pole as the man was standing on the same street has a angle of elevation from the tip of her shadow to her head of 24°. If the two people are 20 feet apart, how far is the street light from the head of the woman?

Let 
A> angle of elevation of the shadow of a man> 28°
B> angle of elevation of the shadow of a woman> 24°
c=20 ft
C=180-(A+B)> C=180-(28+24)> 128°

applying the law of sines
20/sin C=a/sin A> a=20*sin 28/sin 128> a=11.92 ft> a=11.9 ft

the answer part 3) is the option
C)The street light is 11.9 feet from the head of the woman.

Part 4) Solve the triangle: a = 7, b = 9, C = 100°. If it is not possible, say so.

applying the law of cosines
c²=a²+b²-2*a*b*cos C> c²=7²+9²-2*7*9*cos 100°> c²=151.88
c=12.3

applying the law of sines
c/sin C=b/sin B> c*sin B=b*sin C> sin B=(b/c)*sin C
sin B=(9/12.3)*sin 100> sin B=0.7206
B=arc sin (0.7206)> B=46.1°
A=180-(100+46.1)> A=33.9°
so
a=7  b=9  c=12.3
A=33.9°  B=46.1°  C=100°

the answer part 4) is the option
D) A=34, B=46, C=12.3

Part 5)The triangle described is of the form SSA. Determine if there is no triangle possible, one triangle possible, or two triangles possible. If only one triangle is possible, solve the triangle. If either two triangles may be formed or no triangle may be formed, say so. The triangle is defined by: a=10, b=12, B=45
applying the law of sines
b/sin B=a/sin A> sin A=(a/b)*sin B---> (10/12)*sin 45--> 0.5892
A=arc sin (0.5892)> A=36.1°
C=180-(45+36.1)> C=98.9°
b/sin B=c/sin C> c=b*sin C/sin B> c=12*sin 98.9/sin 45
c=16.77> c=16.8
so
a=10  b=12  c=16.8
A=36.1°  B=45°  C=98.9°

the answer part 5) is the option
A)a=36.1, y=98.9, c=16.8

Part 6) Solve the triangle: a = 8, b = 10, c = 3. If it is not possible, say so.

applying the law of cosines
c²=a²+b²-2*a*b*cos C> cos C=[a²+b²-c²]/[2*a*b]
cos C=[8²+10²-3²]/[2*8*10]> 0.96875
C=arc cos (0.96875)> C=14.4°

applying the law of sines
c/sin C=b/sin B> sin B=(b/c)*sin C---> (10/3)*sin 14.4---> sin B=0.8290
B=arc sin(0.8290)> B=56°
A=180-(14.4+56)> A=109.6°
so
first triangle
A=109.6°  B=56°  C=14.4°

second triangle
C=14.4°
B=180-56=124°
A=180-(14.4+124)---> A=41.6

the answer part 6) is the option
B) A=41.4, B=124.2, C=14.4

Part 7)If possible, find the area of the triangle defined by the following: b = 11, c = 8, a = 28°.

The area of the triangle will be given by:
Area=1/2b*c sin A> Area=(1/2)*11*8*sin 28> 20.7 units²

the answer part 7) is the option
B) 20.7 square units

Part 8)For the function given, state the starting point for a sample period: ƒ(t) = 0.2sin (t − 0.3) + 0.1.

we know that
for t=0.3
ƒ(t) = 0.2sin (0.3 − 0.3) + 0.1> f(t)=0.2*sin (0)+0.1> 0.1
f(t)=0.1
so 
the point is
(0.3,0.1)

the answer Part 8) is the option
D) (0.3, 1)

Part 9)The triangle described is of the form SSA. Determine if there is no triangle possible, one triangle possible, or two triangles possible. If only one triangle is possible, solve the triangle. If either two triangles may be formed or no triangle may be formed, say so. The triangle is defined by: a=10, c=8, B=30

applying the law of cosines
b²=a²+c²-2*a*c*cos B> b²=10²+8²-2*10*8*cos 30> b²=25.44
b=5.04
applying the law of sines
b/sin B=a/sin A> sin A=(a/b)*sin B> (10/5.04)*sin 30
sin A=0.9920
A=arc sin (0.9920)> A=82.8°
C=180-(82.8+30)> C=67.2°

the first triangle dimensions are
a=10  b=5.04    c=8
A=82.8°  B=30°  C=67.2°

second triangle
A=180-82.8> 97.2°
B=30°
C=180-(97.2+30)> C=52.8

the answer part 9) is 
A) Two triangles may be formed

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