Table of Contents
What is the angle p in ABCABC?
ABC is a equilateral triangle therefore all the angles are 60° .And P is a point inside the triangle. And we have to find the area of the triangle. Hint: Reflect P in A B, B C and C A to obtain points X, Y and Z respectively.
How do you find the length of an altitude from P?
P P is any point inside an equilateral triangle, the sum of its distances from three sides is equal to the length of an altitude of the triangle: The sum of the three colored lengths is the length of an altitude, regardless of P’s position
What are the advanced properties of equilateral triangles?
Advanced Properties. An equilateral triangle is drawn so that no point of the triangle lies outside ABCD. The maximum possible area of such a triangle can be written in the form p q√ −r, where p,q, and r are positive integers, and q is not divisible by the square of any prime number. Find p+q+r.
Is there an equilateral triangle in the plane with integer coordinates?
Show that there is no equilateral triangle in the plane whose vertices have integer coordinates. Suppose that there is an equilateral triangle in the plane whose vertices have integer coordinates. The determinant formula for area is rational, so if the all three points are rational points, then the area of the triangle is also rational.
What is the cosine of triangle APC and APB?
Triangle APC has sides x, 30, and 80, with angle APC we’ll call t. Meanwhile, triangle APB has sides x, 50, and 80, with angle APB we observe to be equal in degrees to 180 degrees minus angle APC, Hence, the angles APB and APC have cosines that are the negatives of each other, because
How do you find the equilateral triangle of a plane?
\\angle BPC ∠BP C in degrees. Another property of the equilateral triangle is Van Schooten’s theorem: MA=MB+MC. M A = M B+M C. Here is an example related to coordinate plane. Show that there is no equilateral triangle in the plane whose vertices have integer coordinates.