Question

Find the value of xin the triangle shown below

Answer 1

Answer:

$x=80^{\circ}$

Step-by-step 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:

$\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}$, for any triangle.

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

$\frac{\sin x}{18}=\frac{\sin 50^{\circ}}{14}$.

Solving, we get:

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