in a triangle ABC, BPvie perpendicular to the side AC angle A=60 degree and angle C=45degree
find AP an BP
find area of triangle ABC
what is the perimeter of triangleABC
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Answer:
First find angle B:
B = 180 - (60 + 45) = 75°
Now use the sine rule (law of sines):
BC/sin60° = 6/sin75°
BC * (1 + √3)/(2√2) = 6 * √3/2
BC = (3√3)/ (1 + √3)/(2√2)
BC = (6√6)/(1 + √3) * (1 - √3)/(1 - √3)
BC = (6√6 - 6√18)/(1 - 3)
BC = (6√6 - 18√2)/-2
BC = 9√2 - 3√6 cm
And for AB:
AB/sin45° = 6/sin75°
should get:
AB = 6(√3 - 1) cm
Step-by-step explanation:
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