Question

in $delta tuv$, $t = 70$ inches, $mangle t = 99^{circ}$ and $mangle u = 53^{circ}$. find the length of $u$, to the nearest inch.

Explanation:

Step1: Find angle V

In a triangle, the sum of interior angles is 180°. So, $m\angle V=180^{\circ}-m\angle T - m\angle U$.
$m\angle V = 180^{\circ}-99^{\circ}-53^{\circ}=28^{\circ}$

Step2: Use the Law of Sines

The Law of Sines states that $\frac{t}{\sin T}=\frac{u}{\sin U}$.
We know $t = 70$, $\sin T=\sin99^{\circ}\approx0.9877$, $\sin U=\sin53^{\circ}\approx0.7986$.
From $\frac{t}{\sin T}=\frac{u}{\sin U}$, we can solve for $u$: $u=\frac{t\sin U}{\sin T}$.

Step3: Calculate the value of u

$u=\frac{70\times0.7986}{0.9877}=\frac{55.902}{0.9877}\approx57$

Answer:

57