Trigonometry
Initial explanation
For a right triangle, depending on the location of the angle we are going to use, the sides receive different names:
This time, we have:
opposite side = 70 ft
hypotenuse = x
angle = 64º
Sine equation
We have that the equation of Sine is given by:
[tex]\sin (\text{angle)}=\frac{\text{opposite}}{\text{hypotenuse}}[/tex]
Then, in this case:
[tex]\sin (64º)=\frac{70\text{ ft}}{x}[/tex]
Since
sin(64º) = 0.89879
Then
[tex]\begin{gathered} 0.89879=\frac{70\text{ ft}}{x} \\ \downarrow \\ 0.89879x=70\text{ ft} \\ \downarrow \\ x=\frac{70\text{ ft}}{0.89879}=77.88\text{ ft} \end{gathered}[/tex]
We want to find the nearest tenth of a foot, this means, our answer must have just one number after the decimal point.
Since 77.88 ≅ 77.9.
Then x = 77.9 ft
Answer: x = 77.9 ft
