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Section exercises

Verbal

Describe the altitude of a triangle.

The altitude extends from any vertex to the opposite side or to the line containing the opposite side at a 90° angle.

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Compare right triangles and oblique triangles.

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When can you use the Law of Sines to find a missing angle?

When the known values are the side opposite the missing angle and another side and its opposite angle.

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In the Law of Sines, what is the relationship between the angle in the numerator and the side in the denominator?

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What type of triangle results in an ambiguous case?

A triangle with two given sides and a non-included angle.

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Algebraic

For the following exercises, assume α is opposite side a , β is opposite side b , and γ is opposite side c . Solve each triangle, if possible. Round each answer to the nearest tenth.

α = 43° , γ = 69° , a = 20

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α = 35° , γ = 73° , c = 20

  β = 72° , a 12.0 , b 19.9

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α = 60° , β = 60° , γ = 60°

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a = 4 , α = 60° , β = 100°

  γ = 20° , b 4.5 , c 1.6

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b = 10 , β = 95° , γ = 30°

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For the following exercises, use the Law of Sines to solve for the missing side for each oblique triangle. Round each answer to the nearest hundredth. Assume that angle A is opposite side a , angle B is opposite side b , and angle C is opposite side c .

Find side b when A = 37° , B = 49° , c = 5.

b 3.78

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Find side a when A = 132° , C = 23° , b = 10.

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Find side c when B = 37° , C = 21 , b = 23.

c 13.70

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For the following exercises, 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.

α = 119° , a = 14 , b = 26

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γ = 113° , b = 10 , c = 32

one triangle, α 50.3° , β 16.7° , a 26.7

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b = 3.5 , c = 5.3 , γ = 80°

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a = 12 , c = 17 , α = 35°

two triangles,   γ 54.3° , β 90.7° , b 20.9 or   γ 125.7° , β 19.3° , b 6.9

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a = 20.5 , b = 35.0 , β = 25°

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a = 7 , c = 9 , α = 43°

two triangles,   β 75.7° ,   γ 61.3° , b 9.9 or   β 18.3° , γ 118.7° , b 3.2

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a = 7 , b = 3 , β = 24°

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b = 13 , c = 5 , γ = 10°

two triangles, α 143.2° , β 26.8° , a 17.3 or α 16.8° , β 153.2° , a 8.3

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a = 2.3 , c = 1.8 , γ = 28°

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β = 119° , b = 8.2 , a = 11.3

no triangle possible

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For the following exercises, use the Law of Sines to solve, if possible, the missing side or angle for each triangle or triangles in the ambiguous case. Round each answer to the nearest tenth.

Find angle A when a = 24 , b = 5 , B = 22°.

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Find angle A when a = 13 , b = 6 , B = 20°.

A 47.8° or A 132.2°

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Find angle B when A = 12° , a = 2 , b = 9.

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For the following exercises, find the area of the triangle with the given measurements. Round each answer to the nearest tenth.

a = 5 , c = 6 , β = 35°

8.6

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b = 11 , c = 8 , α = 28°

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a = 32 , b = 24 , γ = 75°

370.9

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a = 7.2 , b = 4.5 , γ = 43°

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Graphical

For the following exercises, find the length of side x . Round to the nearest tenth.

For the following exercises, find the measure of angle x , if possible. Round to the nearest tenth.

A triangle. One angle is 22 degrees with side opposite = 5. Another angle is x degrees with opposite side = 13.

x = 76.9° or  x = 103.1°

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Notice that x is an obtuse angle.

A triangle. One angle is 55 degrees with side opposite = 21. Another angle is x degrees with opposite side = 24.

110.6°

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For the following exercises, find the area of each triangle. Round each answer to the nearest tenth.

A triangle. One angle is 93 degrees with opposite side = 32.6. Another side is 24.1.

A 39.4 ,   C 47.6 ,   B C 20.7  

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Extensions

Find the radius of the circle in [link] . Round to the nearest tenth.

A triangle inscribed in a circle. Two of the legs are radii. The central angle formed by the radii is 145 degrees, and the opposite side is 3.
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Find the diameter of the circle in [link] . Round to the nearest tenth.

A triangle inscribed in a circle. Two of the legs are radii. The central angle formed by the radii is 110 degrees, and the opposite side is 8.3.

10.1

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Questions & Answers

sinx sin2x is linearly dependent
cr Reply
what is a reciprocal
Ajibola Reply
The reciprocal of a number is 1 divided by a number. eg the reciprocal of 10 is 1/10 which is 0.1
Shemmy
 Reciprocal is a pair of numbers that, when multiplied together, equal to 1. Example; the reciprocal of 3 is ⅓, because 3 multiplied by ⅓ is equal to 1
Jeza
each term in a sequence below is five times the previous term what is the eighth term in the sequence
Funmilola Reply
I don't understand how radicals works pls
Kenny Reply
How look for the general solution of a trig function
collins Reply
stock therom F=(x2+y2) i-2xy J jaha x=a y=o y=b
Saurabh Reply
sinx sin2x is linearly dependent
cr
root under 3-root under 2 by 5 y square
Himanshu Reply
The sum of the first n terms of a certain series is 2^n-1, Show that , this series is Geometric and Find the formula of the n^th
amani Reply
cosA\1+sinA=secA-tanA
Aasik Reply
Wrong question
Saad
why two x + seven is equal to nineteen.
Kingsley Reply
The numbers cannot be combined with the x
Othman
2x + 7 =19
humberto
2x +7=19. 2x=19 - 7 2x=12 x=6
Yvonne
because x is 6
SAIDI
what is the best practice that will address the issue on this topic? anyone who can help me. i'm working on my action research.
Melanie Reply
simplify each radical by removing as many factors as possible (a) √75
Jason Reply
how is infinity bidder from undefined?
Karl Reply
what is the value of x in 4x-2+3
Vishal Reply
give the complete question
Shanky
4x=3-2 4x=1 x=1+4 x=5 5x
Olaiya
hi can you give another equation I'd like to solve it
Daniel
what is the value of x in 4x-2+3
Olaiya
if 4x-2+3 = 0 then 4x = 2-3 4x = -1 x = -(1÷4) is the answer.
Jacob
4x-2+3 4x=-3+2 4×=-1 4×/4=-1/4
LUTHO
then x=-1/4
LUTHO
4x-2+3 4x=-3+2 4x=-1 4x÷4=-1÷4 x=-1÷4
LUTHO
A research student is working with a culture of bacteria that doubles in size every twenty minutes. The initial population count was  1350  bacteria. Rounding to five significant digits, write an exponential equation representing this situation. To the nearest whole number, what is the population size after  3  hours?
David Reply
f(x)= 1350. 2^(t/20); where t is in hours.
Merkeb
Practice Key Terms 4

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Source:  OpenStax, Algebra and trigonometry. OpenStax CNX. Nov 14, 2016 Download for free at https://legacy.cnx.org/content/col11758/1.6
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