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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

f(x)=x square-root 2 +2x+1 how to solve this value
Marjun Reply
what is algebra
Ige Reply
The product of two is 32. Find a function that represents the sum of their squares.
Paul
if theta =30degree so COS2 theta = 1- 10 square theta upon 1 + tan squared theta
Martin Reply
how to compute this 1. g(1-x) 2. f(x-2) 3. g (-x-/5) 4. f (x)- g (x)
Yanah Reply
hi
John
hi
Grace
what sup friend
John
not much For functions, there are two conditions for a function to be the inverse function:   1--- g(f(x)) = x for all x in the domain of f     2---f(g(x)) = x for all x in the domain of g Notice in both cases you will get back to the  element that you started with, namely, x.
Grace
sin theta=3/4.prove that sec square theta barabar 1 + tan square theta by cosec square theta minus cos square theta
Umesh Reply
acha se dhek ke bata sin theta ke value
Ajay
sin theta ke ja gha sin square theta hoga
Ajay
I want to know trigonometry but I can't understand it anyone who can help
Siyabonga Reply
Yh
Idowu
which part of trig?
Nyemba
functions
Siyabonga
trigonometry
Ganapathi
differentiation doubhts
Ganapathi
hi
Ganapathi
hello
Brittany
Prove that 4sin50-3tan 50=1
Sudip Reply
f(x)= 1 x    f(x)=1x  is shifted down 4 units and to the right 3 units.
Sebit Reply
f (x) = −3x + 5 and g (x) = x − 5 /−3
Sebit
what are real numbers
Marty Reply
I want to know partial fraction Decomposition.
Adama Reply
classes of function in mathematics
Yazidu Reply
divide y2_8y2+5y2/y2
Sumanth Reply
wish i knew calculus to understand what's going on 🙂
Dashawn Reply
@dashawn ... in simple terms, a derivative is the tangent line of the function. which gives the rate of change at that instant. to calculate. given f(x)==ax^n. then f'(x)=n*ax^n-1 . hope that help.
Christopher
thanks bro
Dashawn
maybe when i start calculus in a few months i won't be that lost 😎
Dashawn
what's the derivative of 4x^6
Axmed Reply
24x^5
James
10x
Axmed
24X^5
Taieb
comment écrire les symboles de math par un clavier normal
SLIMANE
Thanks for this helpfull app
Axmed Reply
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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