Geometry | Mathematics problem solving skills

Geometry is an essential branch of mathematics, which makes it important for any student to have a detailed, well-rounded knowledge of trigonometry that covers a variety of topics. Geometry is the fourth math course in high school and will guide you through among other things points, lines, planes, angles, parallel lines, triangles, similarity, trigonometry, quadrilaterals, transformations, circles and area. This Geometry math course is divided into 10 chapters and each chapter is divided into several lessons. Under each lesson you will find theory, examples and video lessons. Talent Academy hopes that you will enjoy studying Geometry online with us!

Sample of some problem with their solution from this courses.

Pro :- Two angles of a triangle measure 30 and 45 degrees. If the side of the triangle opposite the 30-degree angle measures 6√ 2 units, what is the sum of the lengths of the two remaining sides?
Sol ;- Given that two angles of a triangle measure 30 and 45 degrees with side of the triangle opposite the 30-degree angle measures 6√ 2 units,  draw  a perpendicular line from point B to point D which creates a two right angle triangles. Consider  right angle triangle  BCD ,  whose angles at D and B is 90 and 45 respectively.  let angle at C be "S", the sum of  angles of  a triangle is 180, therefore the sum of triangles in triangle BCD is, S+ 45 + 90 =180; S= 45.  Triangle BCD is a isosceles right angle triangle, the hypogenous is given as BC =  6$\sqrt{2}$, let  CD and DB be  length "X" respectively, using Pythagoras theorem  we get ,  CD^2 + BD^2 =  BC^2; X^2 +X^2 = (6$\sqrt{2}$)^2; we get X = 6.  Now consider right angle triangle  ADC ,  whose angles at D and A is 90 and 30 respectively.  let angle at C be "Z", the sum of  angles of  a triangle is 180, therefore the sum of triangles in triangle ADC is, Z + 30 + 90 =180; Z = 60.  Triangle ADC is a right angle triangle, from the previous step we know that length of  CD is  6 , extend CD and A  till they meet at point  P of angle 60, we a equilateral triangle. We see CD + DP = CP = 12, therefore sides of CA and AP  are length of 12. Let  AD be Q , using Pythagoras theorem in triangle ADC  we get ,  CD^2 + Q^2 =  AC^2; 6^2 +Q^2 = (12)^2; we get Q = 6$\sqrt{3}$, therefore the sum of the sides of the triangle ABC is,  AB + BC + CA = 18+6*√ 3

Que :- A cylindrical jar with height 8 inches and diameter 6 inches is filled to 75% of its capacity with juice. The juice is then poured into another cylindrical container with a 10 inch diameter and height of 4 inches. To what percent of its capacity is the second jar filled with juice? (Mathcouns Competitions).
Ans ;54 (percent)

From architecture to engineering, trigonometry is widely used in several common careers. Gaining an understanding of trigonometry opens a wide range of doors in the field of mathematics for students interested in continuing their study.

Talent academy makes sure to cover all concepts and has divided the courses based on students interest, students can enroll to the necessary schedule.

• Geometry
• Mini Geometry
• ADV. Geometry