Always draw a diagram (it's worth marks)
Bisect the vertex with a vertical line which is the ht -
use the half angle (a) to calculate half the base -
which will be equal to Tan (a) x ht
Height=100m
Vertex angle=0.007⁰ a = 0.0035⁰
Base=2 x 100 x tan 0.0035 = 0.0122m
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The base angles of an isosceles triangle will always be equal and have a value of:
b=(180-v)/2 and since you know the height you can say:
tanb=h/(B/2)=2h/B so:
tan((180-v)/2)=2h/B
B=2h/tan((180-v)/2)...in this case:
B=2(100)/tan(89.9965)
B~0.0122m (you sure .007 is the vertex angle :P)
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Draw a diagram.
height h
base b
vertex angle α
Drop a perpendicular from the vertex to the base.
This makes two right-angled triangles.
Each of these has:
one angle α/2
one side h and
the other perpendicular side b/2
From your diagram and the definition of tangent:
tan(α/2) = (b/2)/h = b/(2h)
b = 2htan(α/2)
That's the formula.
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In your example:
b = 2 x 100 x tan(0.0035⁰)
. .= 0.012m
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If you need a formula for that, then you're doing something wrong.
Do you even know trig? This is basics. DRAW the triangle, set up a proportion and *work out* the formula.
Best wishes!
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Height h cm; base b cm; vertex angle 2θ (2 for convenience)
then b/2 = h * tan θ,
b = 2h * tan θ,
Your example (m, not cm)
b = 200 * tan 0.0035°, = 0.0122
base is 1.22 cm