The length of FD = 0.76 feet.
Step-by-step explanation:
Given that in ΔDEF, the angle F measures 90° and the angle D measures 83° and EF=6.2 feet
To find the length of FD, let us use the tangent function. The tangent of an angle is the length of opposite side divided by the length of the adjacent side.
[tex]\tan \theta=\frac{o p p}{a d j}[/tex]
From the given data, θ=83°, [tex]o p p=6.2[/tex] and [tex]a d j=x[/tex]
Substituting these values in the tangent formula, we get,
[tex]\begin{array}{r}{\tan \theta=\frac{o p p}{a d j}} \\{\tan 83^{\circ}=\frac{6.2}{x}}\end{array}[/tex]
Using calculator, the value of [tex]\tan 83^{\circ}=8.14[/tex] and substituting and solving the equation, we get,
[tex]\begin{aligned}8.14 &=\frac{6.2}{x} \\x &=\frac{6.2}{8.14} \\x &=0.76\end{aligned}[/tex]
Thus, the length of FD = 0.76 feet.
