What are the three situations when you can use the law of sines.
1 you are given a triangle with two angles and the included side.
2 you are given a triangle with all three sides.
3 you are given a triangle with two sides and a non-included angle.
4 you are given a triangle all three angles.
5 you are given a triangle with two angles and a non-included side.

Answer with explanation:

Law of Sines

If the triangle has side length, a , b and c and Angles are A, B and C , then Sine law can be written as

1. You are given a triangle with two angles and the included side.

Find the measure of third Angle, then using sine law find the length of other sides.

3.You are given a triangle with two sides and a non-included angle.

  First evaluate , second angle which is in front of corresponding side and then third angle and other side.

5.You are given a triangle with two angles and a non-included side.

Calculate the third Angle using angle sum property and other sides using sine law.

b. an equilateral triangle inscribed in a circle

step-by-step explanation:

we are given the figure of two circles having a triangle inside.

now, we know that,

"when a figure is lying inside an another figure, then the outside figure is known as circumscribed figure and the figure lying inside is referred to as the inscribed figure".

as we see that, the circles are containing the triangle completely.

thus, the circles are the circumscribed figures and the triangle is the inscribed figure.

hence, we get, 'an equilateral triangle is inscribed in a circle'.

hello from mrbilldoesmath!

answer:

25x^2 + 90x + 84

discussion:

mn(x) = m(n(x)) = m( 5x + 9) =

(5x + 9)^2 + 3 =>

25x^2 + 90x + 9^2 + 3 =

25x^2 + 90x + 84                 (as 9^2 = 9*9 = 81)

which is the second choice

regards,  

mrb

p.s.   i'll be on vacation from friday, dec 22 to jan 2, 2019. have a great new year!