Question

HELPPPPP ASAP!!!! Thx!! and NOOO FILESSSS!!

Answer 1

`x=32`°

Explanation:

The law of sines is a property of all triangles that relates the sides and angles of a triangle. This property states the following:

`(sin(a))/(A)=(sin(b))/(B)=(sin(c))/(C)`

Where side (A) is the side opposite angle (<a), side (B) is the side opposite angle (<b), and side (C) is the property opposite angle (<c).

Substitute each of the sides and respective angles into the formula, and solve for the unknown angle (<x). Please note that a triangle with two congruent sides (referred to as an isosceles triangle) has a property called the base angles theorem. This states that the angles opposite the congruent sides in an isosceles triangle are congruent. Therefore, there can be two (<x)'s in this triangle.

`(sin(a))/(A)=(sin(b))/(B)=(sin(c))/(C)`

`(sin(x))/(10)=(sin(116))/(17)=(sin(x))/(10)`

One can shorten the equation so it only holds the parts that will play a role in solving this equation,

`(sin(x))/(10)=(sin(116))/(17)`

Now take the cross product in this equation to simplify it further,

`(sin(x))/(10)=(sin(116))/(17)`

`17(sin(x))=10(sin(116))`

Inverse operations, solve this equation for (x),

`17(sin(x))=10(sin(116))`

`sin(x)=(10(sin(116)))/(17)`

`x=sin^-^1((10(sin(116)))/(17))`

`x=31.91782...`

`x\approx32`

Answer 2

hello,

Explanation:

the triangle is isocele,

x+x+116=180

x=(180-116)/2

x= 32° (thirty-two , trente-deux in french)