Answer:
The length of WU is 302.3 feet.
Explanation:
By Geometry we know that sum of internal angles of a triangle equals 180º, then the measure of angle V is:
[tex]\angle V = 180^{\circ}-\angle U - \angle W[/tex] (1)
[tex]\angle V = 180^{\circ}-15^{\circ}-90^{\circ}[/tex]
[tex]\angle V = 75^{\circ}[/tex]
Please notice that segment VW is opposite to angle U and segment WU is opposite to angle V, then we use Law of Sine to calculate the value of the latter segment. All sides are measured in feet:
[tex]\frac{VW}{\sin U} = \frac{WU}{\sin V}[/tex] (2)
If we know that [tex]VW = 81\,ft[/tex], [tex]\angle U = 15^{\circ}[/tex] and [tex]\angle V = 75^{\circ}[/tex], then the length of segment WU is:
[tex]WU = VW \cdot \left(\frac{\sin V}{\sin U} \right)[/tex]
[tex]WU = 302.3\,ft[/tex]
The length of WU is 302.3 feet.
