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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

The sequence is {1,-1,1-1.....} has
amit Reply
circular region of radious
Kainat Reply
how can we solve this problem
Joel Reply
Sin(A+B) = sinBcosA+cosBsinA
Eseka Reply
Prove it
Eseka
Please prove it
Eseka
hi
Joel
June needs 45 gallons of punch. 2 different coolers. Bigger cooler is 5 times as large as smaller cooler. How many gallons in each cooler?
Arleathia Reply
7.5 and 37.5
Nando
find the sum of 28th term of the AP 3+10+17+---------
Prince Reply
I think you should say "28 terms" instead of "28th term"
Vedant
the 28th term is 175
Nando
192
Kenneth
if sequence sn is a such that sn>0 for all n and lim sn=0than prove that lim (s1 s2............ sn) ke hole power n =n
SANDESH Reply
write down the polynomial function with root 1/3,2,-3 with solution
Gift Reply
if A and B are subspaces of V prove that (A+B)/B=A/(A-B)
Pream Reply
write down the value of each of the following in surd form a)cos(-65°) b)sin(-180°)c)tan(225°)d)tan(135°)
Oroke Reply
Prove that (sinA/1-cosA - 1-cosA/sinA) (cosA/1-sinA - 1-sinA/cosA) = 4
kiruba Reply
what is the answer to dividing negative index
Morosi Reply
In a triangle ABC prove that. (b+c)cosA+(c+a)cosB+(a+b)cisC=a+b+c.
Shivam Reply
give me the waec 2019 questions
Aaron Reply
the polar co-ordinate of the point (-1, -1)
Sumit 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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