Question

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 | = | ° |

Answer #1

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,...

Solve for the remaining side(s) and angle(s) if possible. (Round
your answers to two decimal places. If not possible, enter
IMPOSSIBLE.)
α = 3°, a = 63, b = 100
smaller β β
=
°
γ
=
°
c
=
larger β β
=
°
γ
=
°
c
=

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

Find the direction cosines of v=8i-8j+4k and confirm that they
satisfy cos2α+cos2β+cos2γ=1. Then use the direction cosines to
approximate the direction angles to the nearest degree.
Enter the exact answers for the direction cosines.
cos α=
Edit
cos β=
Edit
cos γ=
Edit
α≈ ∘
β≈ ∘
γ≈ ∘

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

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=

Use the Law of Sines to solve for all possible triangles that
satisfy the given conditions. (If an answer does not exist, enter
DNE. Round your answers to one decimal place. Below, enter your
answers so that ∠A1 is smaller than
∠A2.)
b = 26, c = 31, ∠B
= 27°
∠A1 =
°
∠A2 =
°
∠C1 =
°
∠C2 =
°
a1 =
a2 =

Use the Law of Sines to solve for all possible triangles that
satisfy the given conditions. (If an answer does not exist, enter
DNE. Round your answers to one decimal place. Below, enter your
answers so that ∠A1 is smaller than
∠A2.)
b = 29, c = 32, ∠B
= 21°
∠A1 =
°
∠A2 =
°
∠C1 =
°
∠C2 =
°
a1 =
a2 =

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
=
° '

1. Consider the following.
h(x)=x 3sqrt(x-5)
Find the critical numbers. (Enter your answers as a
comma-separated list. If an answer does not exist, enter DNE.)
x =
Find the open intervals on which the function is increasing or
decreasing. Use a graphing utility to verify your results. (Enter
your answers using interval notation. If an answer does not exist,
enter DNE.)
increasing:
decreasing:
2. Compare the values of dy and Δy for the
function. (Round your answers to four decimal...

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