In an isosceles triangle, the base is 15 cm long. The cosine of the angle between the sides is 7/16. What is the side side?
September 15, 2021 | education
| Since the triangle is isosceles, then AB = CB.
Let’s apply the cosine theorem for a triangle.
AC ^ 2 = AB ^ 2 + CB ^ 2 – 2 * AB * CB * CosABC.
152 = 2 * AB ^ 2 – 2 * AB ^ 2 * (7/16).
225 = 2 * AB ^ 2 * (1 – 7/16)
225 = 2 * AB ^ 2 * 9/16 = 9 * AB ^ 2/8.
AB ^ 2 = 225 * 8/9 = 200.
AB = CB = 10 * √2 cm.
Answer: The length of the side is 10 * √2 cm.
One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.