Question

In ASTU, U = 900 cm,

Answer 1

We shall begin by drawing a sketch of the triangle STU as shown below;

As shown in the triangle above, Angle U and side length u is given. Angle S is calculated as follows;

$\begin{gathered} S+T+U=180(\text{angles in a triangle sum up to 180)} \\ S+49+14=180 \\ S=180-49-14 \\ S=117 \\ \text{Having derived angle S, we shall apply the law of sines as follows;} \\ \frac{a}{\sin a}=\frac{b}{\sin b} \\ \text{Substitute for the known values, which are U, S, u and s} \\ \frac{u}{\sin U}=\frac{s}{\sin S} \\ \frac{900}{\sin14}=\frac{s}{\sin 117} \\ \frac{900\times\sin 117}{\sin 14}=s \\ \frac{900\times0.891}{0.2419\ldots}=s \\ \frac{801.9}{0.2419}=s \\ 3315.0062=s \\ s\approx3315 \end{gathered}$

Therefore, the length of s is 3,315 cm