<< Chapter < Page Chapter >> Page >

Explain the relationship between the Pythagorean Theorem and the Law of Cosines.

Got questions? Get instant answers now!

When must you use the Law of Cosines instead of the Pythagorean Theorem?

The Law of Cosines must be used for any oblique (non-right) triangle.

Got questions? Get instant answers now!

Algebraic

For the following exercises, assume α is opposite side a , β is opposite side b , and γ is opposite side c . If possible, solve each triangle for the unknown side. Round to the nearest tenth.

γ = 41.2° , a = 2.49 , b = 3.13

Got questions? Get instant answers now!

α = 120° , b = 6 , c = 7

11.3

Got questions? Get instant answers now!

β = 58.7° , a = 10.6 , c = 15.7

Got questions? Get instant answers now!

γ = 115° , a = 18 , b = 23

34.7

Got questions? Get instant answers now!

α = 119° , a = 26 , b = 14

Got questions? Get instant answers now!

γ = 113° , b = 10 , c = 32

26.7

Got questions? Get instant answers now!

β = 67° , a = 49 , b = 38

Got questions? Get instant answers now!

α = 43.1° , a = 184.2 , b = 242.8

257.4

Got questions? Get instant answers now!

α = 36.6° , a = 186.2 , b = 242.2

Got questions? Get instant answers now!

β = 50° , a = 105 , b = 45

not possible

Got questions? Get instant answers now!

For the following exercises, use the Law of Cosines to solve for the missing angle of the oblique triangle. Round to the nearest tenth.

a = 42 , b = 19 , c = 30 ; find angle A .

Got questions? Get instant answers now!

a = 14 ,   b = 13 ,   c = 20 ; find angle C .

95.5°

Got questions? Get instant answers now!

a = 16 , b = 31 , c = 20 ; find angle B .

Got questions? Get instant answers now!

a = 13 , b = 22 , c = 28 ; find angle A .

26.9°

Got questions? Get instant answers now!

a = 108 , b = 132 , c = 160 ; find angle C .

Got questions? Get instant answers now!

For the following exercises, solve the triangle. Round to the nearest tenth.

A = 35° , b = 8 , c = 11

B 45.9° , C 99.1° , a 6.4

Got questions? Get instant answers now!

B = 88° , a = 4.4 , c = 5.2

Got questions? Get instant answers now!

C = 121° , a = 21 , b = 37

A 20.6° , B 38.4° , c 51.1

Got questions? Get instant answers now!

a = 13 , b = 11 , c = 15

Got questions? Get instant answers now!

a = 3.1 , b = 3.5 , c = 5

A 37.8° , B 43.8 , C 98.4°

Got questions? Get instant answers now!

a = 51 , b = 25 , c = 29

Got questions? Get instant answers now!

For the following exercises, use Heron’s formula to find the area of the triangle. Round to the nearest hundredth.

Find the area of a triangle with sides of length 18 in, 21 in, and 32 in. Round to the nearest tenth.

177.56 in 2

Got questions? Get instant answers now!

Find the area of a triangle with sides of length 20 cm, 26 cm, and 37 cm. Round to the nearest tenth.

Got questions? Get instant answers now!

a = 1 2 m , b = 1 3 m , c = 1 4 m

0.04 m 2

Got questions? Get instant answers now!

a = 12.4  ft ,   b = 13.7  ft ,   c = 20.2  ft

Got questions? Get instant answers now!

a = 1.6  yd ,   b = 2.6  yd ,   c = 4.1  yd

0.91 yd 2

Got questions? Get instant answers now!

Graphical

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

For the following exercises, find the measurement of angle A .

Find the measure of each angle in the triangle shown in [link] . Round to the nearest tenth.

A triangle A B C. Angle A is opposite a side of length 10, angle B is opposite a side of length 12, and angle C is opposite a side of length 7.
Got questions? Get instant answers now!

For the following exercises, solve for the unknown side. Round to the nearest tenth.

For the following exercises, find the area of the triangle. Round to the nearest hundredth.

Extensions

A parallelogram has sides of length 16 units and 10 units. The shorter diagonal is 12 units. Find the measure of the longer diagonal.

Got questions? Get instant answers now!

The sides of a parallelogram are 11 feet and 17 feet. The longer diagonal is 22 feet. Find the length of the shorter diagonal.

18.3

Got questions? Get instant answers now!

The sides of a parallelogram are 28 centimeters and 40 centimeters. The measure of the larger angle is 100°. Find the length of the shorter diagonal.

Got questions? Get instant answers now!

A regular octagon is inscribed in a circle with a radius of 8 inches. (See [link] .) Find the perimeter of the octagon.

An octagon inscribed in a circle.

48.98

Got questions? Get instant answers now!

A regular pentagon is inscribed in a circle of radius 12 cm. (See [link] .) Find the perimeter of the pentagon. Round to the nearest tenth of a centimeter.

A pentagon inscribed in a circle.
Got questions? Get instant answers now!

For the following exercises, suppose that x 2 = 25 + 36 60 cos ( 52 ) represents the relationship of three sides of a triangle and the cosine of an angle.

Find the length of the third side.

Got questions? Get instant answers now!

For the following exercises, find the area of the triangle.

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
Please you teach
Dua
Yes
ahmed
Thank you
Dua
give me treganamentry question
Anshuman Reply
Solve 2cos x + 3sin x = 0.5
shobana Reply
Practice Key Terms 2

Get the best Algebra and trigonometry course in your pocket!





Source:  OpenStax, Algebra and trigonometry. OpenStax CNX. Nov 14, 2016 Download for free at https://legacy.cnx.org/content/col11758/1.6
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Algebra and trigonometry' conversation and receive update notifications?

Ask