Question

Find the value of xin the triangle shown below

Answer 1

`x=80^(\circ)`

Explanation:

Solution 1:

Recall that in an isosceles triangle, the two angles adjacent to the congruent sides are equal. Since the sum of interior angles in a triangle add up to
`180^(\circ)`, we set up the following equation:

`x+50+50=180`.

Solving, we get:

`x+100=80,\\x=\fbox{$80^(\circ)$}`.

Solution 2:

The Law of Sines states:

`(\sin A)/(a)=(\sin B)/(b)=(\sin C)/(c)`, for any triangle.

We can use this to set up a proportion with the information given:

`(\sin x)/(18)=(\sin 50^(\circ))/(14)`.

Solving, we get:

`x=\arcsin((18\cdot \sin 50^(\circ))/(14)),\\x \approx \fbox{$80^(\circ)$}`.