Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 year ago

# Trigonometry Question? (picture attached)? Relevance

The sums of angles in a triangle must be 180. So we can set up these equations based on this:

a + b + c = 180

e + d + 90 = 180 --> e + d = 90

g + h + 90 = 180 --> g + h = 90

The sum of the angles making a straight line is 180, so:

f + b + e = 180

h + 143 = 180 --> h = 37

the line where "a" and "c" are touching and the line where "b", "e", "f", and "h" are touching are parallel, so the connecting perpendicular lines make right angles. This pairs off c and d:

c + d = 90

Also note that the triangle "a", "b", "c" is an equilateral triangle, so the angles are also the same:

a = b = c

So starting with this and the first equation, we can solve for a, which solves for b and c:

a + b + c = 180

a + a + a = 180

3a = 180

a = 60°

b = a --> b = 60°

c = a --> c = 60°

Now we can solve for d:

c + d = 90

60 + d = 90

d = 30°

Now we can solve for e, then f:

e + d = 90

e + 30 = 90

e = 60°

f + b + e = 180

f + 60 + 60 = 180

f + 120 = 180

f = 60°

We've already solved for h when simplifying equations, so finally we can solve for g:

g + h = 90

g + 37 = 90

g = 53°

So all of the angles are:

a = 60°

b = 60°

c = 60°

d = 30°

e = 60°

f = 60°

g = 53°

h = 37°

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• a = 60°, b = 60°, c = 60°, h = 37°, g = 53°,

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• a = b = c = e = f with 60°; d = 30° ; h = 37° ===> g = 53°

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