Step: 1

The length c is longer side and the angle opposite to it is angle C.

Step: 2

Cos C = 4 2 + 3 2 - 5 2 2 ( 4 ) ( 3 )

[Use law of cosines:

Cos C =a 2 + b 2 - c 2 2 a b .]

Cos C =

Step: 3

Cos C = 0 2 4 = 0

Step: 4

Correct Answer is : 90^{o}

Step: 1

[Law of Cosines.]

Step: 2

Cos D = e 2 + f 2 - d 2 2 e f .

Step: 3

Cos D = 1 5 2 + 2 2 2 - 6 2 2 ( 1 5 ) ( 2 2 )

Step: 4

Cos D ≈ 1.019696

Step: 5

Step: 6

Triangle cannot be drawn with the given sides.

Correct Answer is : not possible to find

Step: 1

[Use law of Sines: Sin Q q = Sin P p .]

Step: 2

Sin P = 12 Sin 75 o 17

Step: 3

Sin P = 0.68

Step: 4

Step: 5

The measure of 137^{o} is not possible, since 137^{o} + 75^{o} = 212^{o} and 212^{o} is greater than 180^{o}.

Step: 6

So, ∠ P = 43^{o}.

Step: 7

[Sum of the angle measures in a triangle is 180^{o}.]

Step: 8

Correct Answer is : 62^{o}

Step: 1

[Use law of Cosines.]

Step: 2

Step: 3

[Simplify.]

Step: 4

BC = 15.5

[Simplify.]

Step: 5

The distance between B and C is 15.5 cm.

Correct Answer is : 15.5 cm

Step: 1

[Sum of the measures of angles in a triangle is 180^{o}.]

Step: 2

Step: 3

[Use law of sines: sin A a = sin B b .]

Step: 4

[Simplify.]

Correct Answer is : 23 units

Step: 1

[Using law of cosines:

d 2 = e 2 + f 2 - 2e f cos D.]

Step: 2

Step: 3

[Simplify using calculator.]

Correct Answer is : 8

Step: 1

[Use law of Sines: sin A a = sin B b .]

Step: 2

sin B = 8 sin 6 2 ° 1 4

Step: 3

sin B = 0.50

[Simplify.]

Step: 4

∠B = 30° or 150°

Step: 5

The measure of 150° is not possible, since 150° + 62° = 212° and 212° is greater than 180°.

Step: 6

So, ∠B = 30°.

Step: 7

∠C = 180° - (62° + 30°) = 88°

Step: 8

[Use law of Sines: sin C c = sin A a .]

Step: 9

Correct Answer is : 16 in.

Step: 1

[Use law of Sines : sin P p = sin Q q .]

Step: 2

Sin P = 17 Sin 68° 23

Step: 3

Sin P = 0.7

[Simplify.]

Step: 4

Step: 5

The measure of 136° is not possible, since 136° + 68° = 204° and 204° is greater than 180°.

Step: 6

So, ∠ P = 44°.

Step: 7

[Sum of the angle measures in a triangle is 180^{o}.]

Step: 8

Correct Answer is : 68°

Step: 1

[Use law of Sines: sin A a = sin C c .]

Step: 2

sin A = 11 sin 73 o 17

Step: 3

sin A = 0.62

Step: 4

Step: 5

The measure of 142^{o} is not possible, since 142^{o} + 73^{o} = 215^{o} and 215^{o} is greater than 180^{o}.

Step: 6

So, ∠ A = 38^{o}.

Step: 7

[Sum of the angle measures in a triangle is 180^{o}.]

Step: 8

Correct Answer is : 69^{o}

Step: 1

[Use law of cosines:

d 2 = e 2 + f 2 - 2ef cos D.]

Step: 2

Step: 3

Correct Answer is : 10.29

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