Cosine Rule question

[sjhines]

In triangle ABC, AB=10, BC=5, CA=x and BAC=θ°.

(a) Show that x^2 −20xcosθ+75=0.
(b) Find the range of values of cos θ for which the above equation has real roots.
(c) Hence find the set of values of θ for which it is possible to construct triangle ABC with the given measurements.

Help will be greatly appreciated. Thanks!

 

[Deleted member 4993]

In triangle ABC, AB=10, BC=5, CA=x and BAC=θ°.

(a) Show that x^2 −20xcosθ+75=0.
(b) Find the range of values of cos θ for which the above equation has real roots.
(c) Hence find the set of values of θ for which it is possible to construct triangle ABC with the given measurements.

Help will be greatly appreciated. Thanks!

Start with Law of cosines for triangles:

(BC)² = (AB)² + (AC)² - 2* AB * AC * Cos(BAC)