Question

1. Let the angles of a triangle be *α*, *β*, and
*γ*, with opposite sides of length *a*, *b*,
and *c*, respectively. Use the Law of Cosines and the Law of
Sines to find the remaining parts of the triangle. (Round your
answers to one decimal place.)

*α* = 105°; *b* =
3; *c* = 10

a=

*β= ____* °

*γ= ____* °

*2.* Let the angles of a triangle be *α*,
*β*, and *γ*, with opposite sides of length
*a*, *b*, and *c*, respectively. Use the Law
of Cosines and the Law of Sines to find the remaining parts of the
triangle. (Round your answers to one decimal place.)

*a* = 6; *b* = 8; *c*
= 12

*α= ____* °

*β= ____* °

*γ= ____* °

Answer #1

Let the angles of a triangle be α, β, and
γ, with opposite sides of length a, b,
and c, respectively. Use the Law of Sines to find the
remaining sides. (Round your answers to one decimal place.)
β = 99°; γ =
29°; c = 20

Let the angles of a triangle be α, β, and
γ, with opposite sides of length a, b,
and c, respectively. Use the Law of Cosines to find the
remaining side and one of the other angles. (Round your answers to
one decimal place.)
α = 46°; b =
12; c = 18

Assume α is opposite side a, β is opposite side b, and γ is
opposite side c. Solve the triangle, if possible. Round your
answers to the nearest tenth. (If not possible, enter IMPOSSIBLE.)
α = 60°, β = 60°, γ = 60°
a=
b=
c=

Assume α is
opposite side a, β
is opposite side b,
and γ is opposite
side c. Determine
whether there is no
triangle, one triangle,
or two triangles.
Then solve each
triangle, if possible.
Round each answer
to the nearest
tenth ?=20.5,?=35.0,?=25°

Use the Law of Cosines to find the remaining side and angles if
possible. (Round your answers to two decimal places. If an answer
does not exist, enter DNE.)
a = 8, b = 12, γ = 67.7°
c
=
α
=
°
β
=
°

If a, b, c are the sides of a triangle and A, B, C are the
opposite angles, find ∂A/∂a, ∂A/∂b, ∂A/∂c by implicit
differentiation of the Law of Cosines.

Draw a triangle ABC with the lengths of its sides 6 cm, 8 cm and
9 cm.
(a) Draw the circumcircle of ABC by using the perpendicular
bisectors of the two sides of lengths 6 cm and 8 cm.
(b) Discuss the accuracy of your drawing by drawing the third
perpendicular bisector of ABC.
(c) Use your ruler to estimate the length of the radius of the
circle drawn in (a).
(d) Use your answer in (c) and the extended...

Solve ΔABC. (Round your answer for b to one
decimal place. Round your answers for α and γ to
the nearest 10 minutes. If there is no solution, enter NO
SOLUTION.)
β =
72°10', c =
14.2, a = 86.6
b
=
α
=
° '
γ
=
° '

Let X ∼ Beta(α, β).
(a) Show that EX 2 = (α + 1)α (α + β + 1)(α + β) .
(b) Use the fact that EX = α/(α + β) and your answer to the
previous part to show that Var X = αβ (α + β) 2 (α + β + 1).
(c) Suppose X is the proportion of free-throws made over the
lifetime of a randomly sampled kid, and assume that X ∼ Beta(2,
8)
....

1.a triangular pasture has sides of length 375 feet, 250 feet,
and300 feet.calculate the area of the pasture
2. ambiguous case of the law of sines: two sides and an angle
are given. Determine whether the given information results in one
triangles, two triangles ,or no triganlge at all. clearly show how
you use the law of sines. you do not need to solve the
triangles.
a) a=3, b=7, A=70 degrees. b) a = 20, c= 30,B=40 degrees. c) a...

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