Question

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

Answer 1

Answer:

$x=32$°

Step-by-step 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:

$\frac{sin(a)}{A}=\frac{sin(b)}{B}=\frac{sin(c)}{C}$

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.

$\frac{sin(a)}{A}=\frac{sin(b)}{B}=\frac{sin(c)}{C}$

$\frac{sin(x)}{10}=\frac{sin(116)}{17}=\frac{sin(x)}{10}$

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

$\frac{sin(x)}{10}=\frac{sin(116)}{17}$

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

$\frac{sin(x)}{10}=\frac{sin(116)}{17}$

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

Inverse operations, solve this equation for (x),

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

$sin(x)=\frac{10(sin(116))}{17}$

$x=sin^-^1(\frac{10(sin(116))}{17})$

$x=31.91782...$

$x\approx32$

Answer 2

Answer:

hello,

Step-by-step explanation:

the triangle is isocele,

x+x+116=180

x=(180-116)/2

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