Given: △ABC, m∠A=60° m∠C=45°, AB=8 Find: Perimeter of △ABC, Area of △ABC
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Answered by
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perimeter of triangle
given A 60°C 45°B?
AB= 8
Then A =4 B =4
B=4
given A 60°C 45°B?
AB= 8
Then A =4 B =4
B=4
I hope it help you
I don't understand... you didn't finish the problem. Could you keep working on it? Thank you SO much for your help. I really appreciate it...
Answered by
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Given : m∠A = 60°, m∠C = 45°.
We know that Sum of interior angles of a triangle = 180°.
⇒ m∠A + m∠B + m∠C = 180
⇒ 60 + m∠B + 45 = 180
⇒ 105 + m∠B = 180
⇒ m∠B = 180 - 105
⇒ m∠B = 75°.
Now,
Given, AB = 8. We have to calculate BC and AC:
We have to use the Law of cosines in order to find an unknown angle:
⇒ (a/sinA) = (b/sinB) = (c/sinC)
(i)
⇒ (AB/sinC) = (BC/sinA)
⇒ (8/sin 45°) = (BC/sin 60°)
⇒ (8/0.707) = (BC/0.866)
⇒ 6.928 = 0.707 BC
⇒ BC = 9.799
(ii)
⇒ (AB/sin C) = (AC/sin B)
⇒ (8/sin 45°) = (AC/sin 75°)
⇒ AC = 10.928.
Perimeter of ΔABC
⇒ AB + BC + AC
⇒ 8 + 10.928 + 9.799
⇒ 28.728
Area of ΔABC:
⇒ (1/2) * AB * AC * sin(60)
⇒ (1/2) * 8 * 10.928 * (√3/2)
⇒ 2 * 10.928 * 1.732
⇒ 37.85
Hope it helps!
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