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In RT △ ABC, ∠ a = 90 °, BC = 4, there is an internal angle of 60 ° and point P is a point on the straight line AB which is different from a and B, and ∠ ACB = 30 °, then the length of Pb is? 3 / 4 root 3 / 8 root 3 / 4, there are three answers, but I can't do it,
The test point of this problem is: right triangle with 30 degree angle; Pythagorean theorem. Special topic: classified discussion. Analysis: consider two cases: when ∠ ABC = 60 ° as shown in the figure, by ∠ ABC = 60 ° and using the mutual complement of two acute angles of right triangle, we can get ∠ cab = 30 ° and ∠ PCA = 30 ° and ∠ PCB + ACB
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- 1. In the RT triangle ABC, the angle a is equal to 90 degrees and BC is equal to 4. There is a point P with an internal angle of 60 degrees, which is different from a and B on the straight line AB, and the angle ACP is equal to 30 degrees to find the length of Pb
- 2. As shown in the figure, in RT △ ABC, ∠ ACB = 90 ° AB = 6, P is the point on AB, connect PC, set ∠ BCP = m ∠ ACP, when AP = 3 / 2, whether there is a positive integer m, Make PC perpendicular to ab? If it exists, calculate the value of M. if it does not exist, explain the reason
- 3. As shown in the figure, it is known that △ ABC, P is the point on AB, connecting CP. in the following conditions, △ ACP ∽ ABC cannot be determined as () A. ∠ACP=∠BB. ∠APC=∠ACBC. ACAP＝ABACD. ACAB＝CPBC
- 4. As shown in the figure, it is known that △ ABC, P is a point on edge ab. when connecting CP, (1) ACP satisfies what conditions, △ ACP is similar to △ ABC? (2) AC: AP is full
- 5. As shown in the figure, we know that in △ ABC, P is the point on AB, connecting CP, when the condition is satisfied______ When △ ACP ∽ ABC
- 6. Given the triangle ACP, similar to the triangle ABC, AC = 4, AP = 2, find the length of AB? (PC connected) a P B C
- 7. It is known that △ ABC is an equilateral triangle, P is a point in the triangle, PA = 3, Pb = 4, PC = 5
- 8. It is known that △ ABC is an equilateral triangle, P is a point in the triangle, PA = 3, Pb = 4, PC = 5
- 9. P is a point in the equilateral triangle ABC, PC = 5, PA = 3, Pb = 4, find the degree of angle APB There are only four points a, P, B, C
- 10. It is known that △ ABC is an equilateral triangle, P is a point in the triangle, PA = 3, Pb = 4, PC = 5
- 11. RT △ ABC, in which the angle a is 90 ° and BC is 4, there is an internal angle of 60 ° and the point P is different from the point AB on the straight line AB, and ∠ ACP = 30 °, then the length of Pb is longer
- 12. It is known that in RT △ ABC, ∠ a = 90 °, AB > AC, P is a point on AB, ∠ ACP = ∠ B, AC = 6, Pb = 5, find the sine value of ∠ APC. Draw the figure yourself. Please, everyone!
- 13. In the plane rectangular coordinate system, the circumscribed circle of a (- 2,0), B (2,0), C (1, √ 3) triangle ABC is m, and the equation for finding the circle m is given To process... Online, etc Ellipse x2 / 4 + x2 / 2 = 1, the right focus is F. if P is any point on the circle m which is different from AB and passes through the origin, make the vertical intersection line of PF x = 2, and judge the positional relationship between PQ and circle m by Q
- 14. Point a (0, - 3) point (- 3,0), point C on the x-axis, if the area of triangle ABC is 15, find the coordinates of point C
- 15. In the plane rectangular coordinate system, point a (0,3), point B (0,2), and point C are on the x-axis. If the area of △ ABC is 15, find the area of point C Find the coordinates of point C
- 16. As shown in the figure, in the plane rectangular coordinate system, a (- 1,5), B (- 1,0), C (- 4,3); (1) calculate the area of △ ABC; (2) draw the figure △ a1b1c1 after △ ABC is translated one unit down and five units to the right, and write the coordinates of each vertex
- 17. As shown in the figure, in the plane rectangular coordinate system xoy, given the points a (- 1,5), B (- 1,0), C (- 4,3) (1), we can calculate the area of ABC
- 18. A (0,0), B (- 3, - 4) C (4, - 2), draw these points (done) in the plane rectangular coordinate system, find the area of △ ABC, the first question has been done
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- 20. Dawning school has a triangle shaped flower bed ABC, first you can directly measure ∠ a = 30 °, AC = 40m, BC = 25m, please find out the area of this flower bed