the bottom or base edge b, the top left edge a, the

Jameson Lucero

Jameson Lucero

Answered question

2022-07-12

the bottom or base edge b,
the top left edge a,
the top right edge c.
Let a=c+2 and b=10.

Answer & Explanation

Isla Klein

Isla Klein

Beginner2022-07-13Added 12 answers

Taking the origin as the intersection of a and b, with the equation in terms of the angle θ at that vertex:
Through the cosine law we have:
( a 2 ) 2 = a 2 + 100 20 a cos θ
4 a + 4 = 100 20 a cos θ
a = 96 20 cos θ 4
With our particular setup, a is the radius. So this is a polar equation, where
r ( θ ) = 96 20 cos θ 4 = 24 5 cos θ 1
we can convert to cartesian coordinates if you want:
5 r cos θ r = 24
( 5 r cos θ 24 ) 2 = r 2
( 5 x 24 ) 2 = x 2 + y 2
y 2 = 24 x 2 240 x + 576
y 2 = 24 ( x 5 ) 2 24
( x 5 ) 2 y 2 24 = 1
which is a hyperbola. You want the rightmost branch (so a > 0), which is valid when cos θ < 1 5

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