Applications of the theorems; dot product
Answers are for parents and teachers.
1
Decide the type of the triangle with sides 10, 24, 27.
Obtuse: 100 + 576 = 676 < 729 = 27².
2
Find the area of the triangle with sides 13, 13, 10 using Heron's formula.
60
3
a(5; −2) and b(2; 5). What is a·b?
0
4
A force F(4; 3) moves a body through s(2; −1). What work is done?
5
5
Why does b² + c² < a² hold in an obtuse triangle?
a² = b² + c² − 2bc·cosA and cosA < 0, so −2bc·cosA > 0.