Respuesta :
Law of cosine helps us to know the third side of a triangle. The length of the third side of the ΔHIJ, h is 6.698 inches.
What is the Law of Cosine?
The law of cosine helps us to know the third side of a triangle when two sides of the triangle are already known the angle opposite to the third side is given. It is given by the formula,
[tex]c =\sqrt{a^2 + b^2 -2ab\cdot Cos\theta}[/tex]
where
c is the third side of the triangle
a and b are the other two sides of the triangle,
and θ is the angle opposite to the third side, therefore, opposite to side c.
As it is given that the length of the first two sides of the triangle is i=6.6inches and j=6.4 inches, while the measure of the ∠H=62°. Therefore,
the length of the third side with the help of cosine rule can be written as,
[tex]h =\sqrt{i^2 + j^2 -2ij\cdot Cos(\angle H)}\\\\h =\sqrt{(6.6)^2 + (6.4)^2 -(2 \times 6.6 \times 6.4)\cdot Cos(62^o)}\\\\h = 6.6976 \approx 6.698[/tex]
Hence, the length of the third side of the ΔHIJ, h is 6.698 inches.
Learn more about the Law of Cosine:
https://brainly.com/question/17289163
