Right triangles

1) For the given triangles, a = 14.5m, b = 6.03m and alpha = 55.6 degrees. Find theta. Answer in units of degrees. No picture, but use points (0,0), (5,0), (5,7) for triangle one. The x side is labeld a and the angle near the origin is alpha. Now the second triangle is against the y side or against the side from (5,0) to (5,7). This triangles points are to make it easier are (5,0), (5,7), and say (7,5). theta is in the angle of this second triangle near the x axis or by point (5,0). side b is the opposite of theta

Lattice Point

I need help understanding the following problem set. 1. Mark a point at the intersection of two rulings. The lattice point. Seven units to the right and four units up, mark another. Use a ruler to find the distance from one point to the other, using the distance between two parallel rulings as the unit. What degree of accurancy can be guaranteed? 2. Mark a lattice point. Four untis ot the left and seven units down, mark another. Use a ruler to find the distance form one point to the other. 3. What is the distance from point (4,2) to the point (-3,-2)? Explain the method used.

Gemotric problem need an algebraic proof

Please see the attached file for the actual problem and a graphical illustration. Let ABC be a right triangle with sides a, b, and hypotenuse c. Let r be the radius of the inscribed circle and ra, rb, and rc be the radii of the escribed circles tangent to sides a, b, and c. What "RELATIONSHIPS" can you discover among the lengths r, ra, rb, rc, a, b, and c. Note that r = (a + b - c)/2

Regular Solids

For each of the 5 regular polyhedra, enumerate the number of vertices (v), edges (e), and faces (f), and then evaluate the quantity v - e + f. (One of the most interesting theorems relating to any convex polyhedron is that v - e + f = 2. -> This was given as part of the problem. I am not sure if it is of any value when solving this problem or not.) Please use pictures to illustrate the concept above along with a detailed explanation of your response. Thank you.

shortest possible line segment

If P is any point on the parabola y = x^2 except for the origin, let Q be the point where the normal line intersects the parabola again. Find the shortest possible length of the line segment PQ.