Isosceles 7929

ABCD isosceles trapezoid. A = 6cm, e = 7cm and delta angle = 105 °. Calculate the remaining pages.

Correct answer:

b =  5.4788 cm
c =  3.164 cm
d =  5.4788 cm

Step-by-step explanation:

a=6 cm e=7 cm δ=105 ∘  β=180−δ=180−105=75 ∘  e2 = a2 + b2 − 2ab cos β  72 = 62 +x2 − 2⋅ 6⋅ x⋅ cos (75°)  x2−3.106⋅ x−13=0  x2−3.106⋅ x−13=0 x2−3.106x−13=0  a=1;b=−3.106;c=−13 D=b2−4ac=3.1062−4⋅1⋅(−13)=61.647236 D>0  x1,2​=2a−b±D​​=23.11±61.65​​ x1,2​=1.553±3.925788 x1​=5.478787692 x2​=−2.372787692  b=x1​=5.4788=5.4788 cm

Our quadratic equation calculator calculates it.

cos β = x/b x=b⋅ cos(β)=5.4788⋅ cos(75°)≐1.418 cm c=a−2⋅ x=6−2⋅ 1.418=3.164 cm
d=b=5.4788=5.4788 cm

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