Math Problem Statement

The image contains three geometry problems: 1) Triangle ABC with given sides and angle, 2) Quadrilateral ABCD with specific side lengths and an angle, and 3) Triangle ABC with given angles and side length.

Solution

The image you uploaded contains three geometric problems. Here's a breakdown of each one:

  1. For the triangle ΔABC\Delta ABC:

    • The given information:
      • ACB=γ\angle ACB = \gamma
      • BC=a=5BC = a = 5
      • AC=b=3AC = b = 3
      • AB=c=7AB = c = 7
    • The task is to determine the angles γ\gamma, RR (circumradius), and μ\mu.
  2. For quadrilateral ABCDABCD:

    • The given information:
      • AC=10AC = 10
      • BD=6BD = 6
      • AQB=120\angle AQB = 120^\circ
    • The task is to find the area of triangle AQBAQB and the circumradius of ΔAQB\Delta AQB.
  3. For the triangle ΔABC\Delta ABC:

    • The given information:
      • b=4b = 4
      • α=60\alpha = 60^\circ
      • β=45\beta = 45^\circ
    • The task is to find the angles α\alpha and β\beta, as well as the circumradius.

Let me know which problem you'd like to solve first, or if you need further clarification!

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Triangle Geometry
Circumradius
Area of Triangle
Trigonometry
Angle Calculation

Formulas

Law of Cosines
Area of Triangle Formula
Circumradius Formula

Theorems

Law of Sines
Angle Sum Property of Triangles

Suitable Grade Level

Grades 9-12