Equilateral triangle ABC, P is a point in the triangle, PA is equal to 3, Pb is equal to 5, PC is equal to 4, find the degree of ∠ APC

Rotate △ APC anticlockwise around point C to △ bp'c, connect PP ', so ∠ APC = bp'c, BP' = BP = 3, obviously △ CPP 'is equilateral triangle, so ∠ pp'c = 60, PC = PP' = 4, in △ BPP ', BP = 5, PP' = 4, BP '= 3, BP ^ 2 = PP' ^ 2 + PP '^ 2, so △ BPP' is right triangle, so ∠ BP'p = 90 °, so ∠ B

RELATED INFORMATIONS

1. In RT △ ABC, ∠ ACB = 90 °, ∠ BAC = 30 °, BC = 1, P is a point in △ ABC, and ∠ APC = ∠ BPC = ∠ APB = 120, calculate the value of PA + Pb + PC
2. In the tetrahedral PABC, PA = Pb = PC = 2, APB = BPC = APC = 30 degree In the tetrahedral PABC (P is the vertex), PA = Pb = PC = 2, ∠ APB = ∠ BPC = ∠ APC = 30 °, starting from point a, circling along the tetrahedral surface, and then returning to point a, the shortest distance is
3. In the triangle ABC, the area of BDE, DCE and ACD are 90, 30 and 28 square centimeters respectively?
4. Given that the points D and E are on the sides AB and AC of △ ABC, de / / BC, the area of △ ABC is s, BC = a, and the area of △ ade is S1, the length of De can be obtained (expressed in the algebraic form of the letters s, S1 and a) A D E B C
5. Given that points D and E are on edges AB and AC of △ ABC, de / / BC, the area of △ ABC is s, BC = a, and the area of △ ade is S1, the length of De can be obtained It is represented by the algebraic expression of the letters s, S1 and a
6. In the acute triangle ABC, be is perpendicular to AC, D is the upper point of AB, angle ade = angle c, s triangle ade area is S1, and △ ABC area is S2, then S1 / S2 is
7. If the three sides of a triangle form an arithmetic sequence, the circumference is 36 and the circumference of the inscribed circle is 6 π, then the triangle is a triangle
8. A and B are walking in opposite directions in AB and meet each other in 2 hours. It is known that the speed ratio of a and B is 5:4, so how long can a catch up with B when they are walking in the same direction?
9. The original tonnage ratio of a and B piles of coal is 5:3. If 90 tons are transported from a pile to B pile, then the tonnage of the two piles is equal. How many tons are there in a and B piles?
10. Is the 2.8 ton truck a large truck or a small truck
11. P is any point in the equilateral triangle ABC, PA = 3, Pb = 5, PC = 4, find the angle APC
12. As shown in the figure, it is known that P is a point on the side BC of △ ABC, and PC = 2PB. If ∠ ABC = 45 ° and ∠ APC = 60 °, find the size of ∠ ACB
13. In △ ABC, the angle ABC = 90, ad is the angular bisector, the points E F are on AC ad, and AE = AB EF / / BC prove that bdef is a diamond
14. It is known that AB is parallel to EF, CD, ad is parallel to BC, and BD is bisected
15. As shown in the figure, in △ ABC, ab = AC, e is on AC, and the extension line of ad = AE, de intersects BC at point F
16. As shown in the figure, extend the edge BC of △ ABC to d so that CD = BC, take the midpoint F of AB and the edge DF intersect AC with E, and calculate the value of aeac
17. As shown in the figure, in RT △ ABC, if ∠ C = 90 °, a = 30 °, e is the point on AB, AE: EB = 4:1, EF ⊥ AC is in F, and FB is connected, then the value of Tan ⊥ CFB is equal to () A. 33B. 233C. 533D. 53
18. As shown in the figure, in △ ABC, ad is high, AE and BF are bisectors of angles. They intersect at point O, ∠ a = 50 ° and ∠ C = 60 ° to find ∠ DAC and ∠ boa
19. Ask four quadrant angle sine cosine tangent value is positive or negative
20. Given that alpha is the second quadrant angle, what quadrant angle is alpha What about half alpha