Verified answer

I'll assume that

- c is the hypotenuse is c

- the other legs are a and b

- A is the angle opposite a (I assume this is what you called α)

- B is the angle opposite b

- therefore, C (the angle opposite c) is 90 degrees

1.

sin(A) = a/c

a = c * sin(A)

a = 78.1 * sin(59)

a =~ 66.9 cm

cos(A) = b/c

b = c * cos(A)

b = 78.1 * cos(59)

b =~ 40.2 cm

A + B + C = 180

59 + B + 90 = 180

B = 180 - 59 - 90

B = 31 degrees

2.

tan(A) = a/b

a = b * tan(A)

b = a / tan(A)

b = 46.8 / tan(86)

b = 3.27 ft

sin(A) = a/c

a = c * sin(A)

c = a / sin(A)

c = 46.8 / sin(86)

c = 46.9 ft

A + B + C = 180

86 + B + 90 = 180

B = 180 - 86 - 90

B = 4 degrees

First you have two angles α that have different values.

You should assign different variables to different angles.

Second, you don't say which side is opposite which angle.

Third, you say that you have a right triangle, and two of the angles are 59⁰ and 86⁰. This means third angle is 35⁰. None of these are right angles.

Perhaps you should go back to original problem, and post question exactly as stated.

Sorry I couldn't help, but data is confusing.

--------------------

EDIT:

I just read minx's comment about one side measured in cm and another in ft. This leads me to the conclusion that we are dealing with TWO triangles !!!!

So, assuming in both cases that α is opposite side a and adjacent to side b, and c is the hypotenuse, we get:

--------------------

First triangle: c = 78.1 cm, α = 59°

Missing angle = 180 - 90 - 59 = 31°

sin(α) = a/c

a = c * sin(α)

a = 78.1 cm * sin(59)

a = 66.94 cm

cos(α) = b/c

b = c * cos(α)

b = 78.1 cm * cos(59)

b = 40.22 cm

--------------------

Second triangle: a = 46.8 ft, α = 86°

Missing angle = 180 - 90 - 86 = 4°

sin(α) = a/c

c = a / sin(α)

c = 46.8 ft / sin(86)

c = 46.91 ft

tan(α) = a/b

b = a / tan(α)

b = 46.8 ft / tan(86)

b = 3.27 ft

You have one measure in cms. and one in feet is this right.?

Also if this is a right triangle the measures you have given for angles can't be correct.

needs to specify

whether

a ,c is opposite side adjacent side or hypotenuse

c= 11.9

a(2)=43.2

a(1)= 31

a(3)=4