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Triangle ABC has interior angles (A,B,C) = (50,30,100)°. Sides opposite

(A,B,C) are (a,b,c,). a = 1. Law of sines says a/sinA = b/sinB = c/sinC, ie., 

1/sin50 = b/sin30 = c/sin100. Then b = sin30/sin50 and c = sin(100)/sin50,

ie., b = 1/(2sin50) and c = 2sin50cos50/sin50 = 2cos50. Then (a,b,c) = 

(1, 0.6527036447, 1.285575219). s = (1/2)(a+b+c) = 1.469139432, 

(s-a) = 0.4691394320, (s-b) = 0.8164357874, (s-c) = 0.1835642127.

Now, by Heron's formula, A^2 = s(s-a)(s-b)(s-c), where A is the area of triangle ABC. A^2 = (1.469139432)(0.4691394320)(0.8164357874)*

(0.1835642127) = 0.1032939778 and A = 0.313938048 square units.

The area of a triangle (to the nearest hundredth) with internal angles of 

A = 50, B = 30, a = 1:

Area = 0.32139

apply law of Sin to solve for side b

.... a............b

--------- = ---------

.sinA........sinB....

 ...1.............b

--------- = ---------

.sin(50)...sin(30)

sin(30) = bsin(50)

b = 0.65

solving for Angle C

m∠C + 50  + 30 = 180

m∠C +80 = 180

m∠C = 180 - 80

m ∠C = 100°

 Now solving the Area of triangle using this formula

Area = 1/2absinC

Area = 1/2(1)(0.65)sin(100)

Area = 0.32 square unit.. Answer//

Online triangle calculator:

Sides: a = 1   b = 0.653   c = 1.286

Area: T = 0.321

Perimeter: p = 2.938

Semiperimeter: s = 1.469

Angle ∠ A = α = 50° = 0.873 rad

Angle ∠ B = β = 30° = 0.524 rad

Angle ∠ C = γ = 100° = 1.745 rad

Answer:

0.32 sq. units (to the nearest hundredth)

The question is misleading. I assume angle A is 50 degrees and angle B is 30 degrees (and therefore the third angle, which I'll call C, is 180 - 50 - 30 = 100 degrees), and the length of side "a" is 1.

In that case, the area is:

T = a^2 / (2(cot(B) + cot(C)))

T = 1^2 / (2(cot(30) + cot(100)))

T =~ 0.3214

Why would you ask this question? Lol for one, no triangle has a total internal angle measure of 81°, and further, giving the angles alone is not good enough to find the area of a triangle as there are an infinite amount of similar triangles with those measures.

depends on how the surface is curved..

assuming those numbers refer to degrees

Simple calculator here

https://www.triangle-calculator.com/

(1/2) ( w / 2 ) where w = sin 100° / sin 50° ( base)