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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 gradient function of a curve is 2x+4 and the curve passes through point (1,4) find the equation of the curve
Kc Reply
1+cos²A/cos²A=2cosec²A-1
Ramesh Reply
test for convergence the series 1+x/2+2!/9x3
success Reply
a man walks up 200 meters along a straight road whose inclination is 30 degree.How high above the starting level is he?
Lhorren Reply
100 meters
Kuldeep
Find that number sum and product of all the divisors of 360
jancy Reply
answer
Ajith
exponential series
Naveen
what is subgroup
Purshotam Reply
Prove that: (2cos&+1)(2cos&-1)(2cos2&-1)=2cos4&+1
Macmillan Reply
e power cos hyperbolic (x+iy)
Vinay Reply
10y
Michael
tan hyperbolic inverse (x+iy)=alpha +i bita
Payal Reply
prove that cos(π/6-a)*cos(π/3+b)-sin(π/6-a)*sin(π/3+b)=sin(a-b)
Tejas Reply
why {2kπ} union {kπ}={kπ}?
Huy Reply
why is {2kπ} union {kπ}={kπ}? when k belong to integer
Huy
if 9 sin theta + 40 cos theta = 41,prove that:41 cos theta = 41
Trilochan Reply
what is complex numbers
Ayushi Reply
give me treganamentry question
Anshuman Reply
Solve 2cos x + 3sin x = 0.5
shobana 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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