Maths Ext: Trigonometry 16 June 2021

Mathematics

1 answer:

sveticcg [70]2 years ago

8 0

The expression for (AB)² in terms of y is $(AB)^2=3y^2+6y+4$ .

In trigonometry, the cosine rule states that the square of the length of any side of a given triangle is the sum of the squares of the lengths of the other sides times the product of the lengths of the other two sides. It states that it is equal to the the angle contained between them. The law of cosines is also called the law of cosines or the cosine formula.
Suppose, a, b and c are lengths of the side of a triangle ABC, then $a^2 = b^2 + c^2 - 2bc \ cos \angle x$ where ∠x, is the angle between the sides of the triangle.

In triangle ABC , angle ACB = 120°, AC = y cm and BC = (y + 2) cm.

On applying cosine rule in this triangle , we get

$(AB)^2=(AC)^2+(BC)^2-2(AC)(BC) \cos ACB\\\\(AB)^2=y^2+(y+2)^2-2y(y+2) \ cos120\\\\(AB)^2=y^2+y^2+4y+4-2y(y+2)\times\frac{-1}{2} \\\\(AB)^2=2y^2+4y+4+y^2+2y\\\\(AB)^2=3y^2+6y+4$