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The sum of tthe angles of a triangle is 180° which means the third angle is 180° - (57° + 71°) = 52°

The sine rule gives:

a/sin A = b/sin B = c / sin C

where side a is opposites angle A, etc.

The sine rule can be used to find the lengths of the other two sides when the angles are all known and one side length is known.

Let angle A = 57°, then side a = 14.5 in.

Let angle B = 71° and angle C = 52°

Using the sine rule:

a/sin A = b/ sin B

→ b = a × sin B/sin A

Similarly, c = a × sin C/sin A

→ The perimeter = a + b + c

= a + a × sin B/sin A + a × sin C/sin A

= a(1 + sin B/sin A + sin C/sin A)

= 14.5 in × (1 + sin 71° / sin 57° + sin 52° / sin 57°)

≈ 44.47 in

≈ 44.5 in

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6y ago

It is 44.47 inches.

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Q: What is the perimeter of a triangle when an angle of 57 degrees is opposite to a side of 14.5 inches and has another angle of 71 degrees?
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What is the perimeter of a triangle when an angle of 57 degrees is opposite a side of14.5cm and another angle is 71 degrees?

Using the sine rule in trigonometry its other sides are 13.62cm and 16.35cm both rounded to two decimal places therefore it follows that the perimeter of the triangle is 14.5cm+13.62xm+16.35cm = 44.47cm


What is the area and perimeter of a scalene triangle when angle 75 degrees is opposite to side 25cm with another angle of 42 degrees?

Using the sine rule in trigonometry its area is 192.885 square cm and its perimeter is 65.379 cm both rounded to three decimal places.


What is the perimeter of a triangle if its smallest side is 13.62 mm when two of its angles are 71 degrees and 57 degrees?

Its 3rd angle is 52 degrees which is its smallest angle and opposite to its smallest side and by using the sine rule the perimeter of the triangle works out as 44.45 mm to two decimal places


What is the perimeter of a scalene triangle when its longest side is 162cm with angles of 37.25 degrees and 48.4 degrees?

Its longest side of 162cm is opposite to its biggest angle which is 94.54 degrees and by using the sine rule its other sides are 98.34cm and 121.49cm. Therefore perimeter of the triangle is: 162+98.34+121.49 = 381.83cm


What is the perimeter of triangle if its longest side is 162cm when two of its angles are 37.25 degrees and 48.4 degrees?

The largest angle then will be 94.35 degrees opposite the longest sides of 162cm and by using the sine rule of 120/sin(94.35) = b/sinB = c/sinC the perimeter of the triangle works out as 381.83cm rounded to two decimal places.

Related questions

What is the perimeter of a triangle when side 14.5cm is opposite angle 57 degrees and has another angle of 71 degrees?

Using the trigonometry sine rule the other sides of the triangle are 16.35cm and 13.62cm so it follows that its perimeter is 14.5+16.35+13.62 = 44.47cm


What is the perimeter of a triangle when an angle of 57 degrees is opposite a side of14.5cm and another angle is 71 degrees?

Using the sine rule in trigonometry its other sides are 13.62cm and 16.35cm both rounded to two decimal places therefore it follows that the perimeter of the triangle is 14.5cm+13.62xm+16.35cm = 44.47cm


What is the area and perimeter of a scalene triangle when angle 75 degrees is opposite to side 25cm with another angle of 42 degrees?

Using the sine rule in trigonometry its area is 192.885 square cm and its perimeter is 65.379 cm both rounded to three decimal places.


What is the perimeter of a triangle if its smallest side is 13.62 mm when two of its angles are 71 degrees and 57 degrees?

Its 3rd angle is 52 degrees which is its smallest angle and opposite to its smallest side and by using the sine rule the perimeter of the triangle works out as 44.45 mm to two decimal places


What is the perimeter of a triangle when side 14.5cm is opposite angle 57 degrees which has another angle of 71degrees?

The 3rd angle must be 52 degrees and so by using the sine rule in trigonometry its other sides are 16.35cm and 13.62cm both rounded to two decimal places. Therefore the perimeter of the triangle is: 14.5+16.35+13.62 = 44.47cm


What does the perimeter have to equal in a triangle?

180 degrees


What is the perimeter of a scalene triangle when its longest side is 162cm with angles of 37.25 degrees and 48.4 degrees?

Its longest side of 162cm is opposite to its biggest angle which is 94.54 degrees and by using the sine rule its other sides are 98.34cm and 121.49cm. Therefore perimeter of the triangle is: 162+98.34+121.49 = 381.83cm


What is the perimeter of triangle if its longest side is 162cm when two of its angles are 37.25 degrees and 48.4 degrees?

The largest angle then will be 94.35 degrees opposite the longest sides of 162cm and by using the sine rule of 120/sin(94.35) = b/sinB = c/sinC the perimeter of the triangle works out as 381.83cm rounded to two decimal places.


Triangle with a perimeter of 9 and a angle of 60 with a similar triangle with a perimeter of 12 what is the angle degree of the second triangle?

== == The corresponding angle is 60 degrees.


What is the perimeter of a triangle when angle 57 degrees is opposite side 14.5 cm which is adjacent to angle 71 degrees?

Using the sine rule in trigonometry of 14.5/sin(57) = b/sin(71) = c/sin(52) the perimeter of the triangle works out as 44.47 cm to two decimal places.


A right triangle has the hypotenuse 12cm and an angle 30 degrees what is the opposite angle?

A right triangle with a hypotenuse of 12cm and an angle 30 degrees has an opposite angle of: 60 degrees.


What is the perimeter of a triangle when its longest side is 162cm with angles of 37.25 degrees and 48.4 degrees?

Using the sine rule in trigonometry the perimeter of the triangle works out as 382cm rounded to the nearest integer