Question

find the value of x in the triangle shown below.
x = \boxed{\space}^\circ
(there is a triangle with side lengths 3.5, 3.5, 4, and angles x°, 55° as shown in the image)

Explanation:

Step1: Identify triangle type & law

This is an isosceles triangle, use the Law of Sines: $\frac{\sin x}{4} = \frac{\sin 55^\circ}{3.5}$

Step2: Rearrange to solve for $\sin x$

$\sin x = \frac{4 \times \sin 55^\circ}{3.5}$

Step3: Calculate numerator first

$\sin 55^\circ \approx 0.8192$, so $4 \times 0.8192 = 3.2768$

Step4: Compute $\sin x$ value

$\sin x = \frac{3.2768}{3.5} \approx 0.9362$

Step5: Find $x$ via arcsine

$x = \arcsin(0.9362) \approx 69.4^\circ$
(Verify: Check triangle angle sum, the third angle is $180 - 69.4 - 55 = 55.6^\circ$, consistent with side lengths)

Answer:

$69.4$ (rounded to one decimal place, or $69^\circ$ if rounding to whole degrees)