Answer:
[tex]\tan(X)=\dfrac{77}{36}[/tex]
Step-by-step explanation:
First we need to find the length of side WX.
To do this, use Pythagoras' Theorem: [tex]a^2+b^2=c^2[/tex]
(where a and b are the legs, and c is the hypotenuse, of a right triangle)
[tex]\implies WX^2+77^2=85^2[/tex]
[tex]\implies WX^2=85^2-77^2[/tex]
[tex]\implies WX=\sqrt{85^2-77^2}[/tex]
[tex]\implies WX=36[/tex]
Now use the Tan trig ratio:
[tex]\tan(x)=\sf \dfrac{O}{A}[/tex]
where:
- [tex]x[/tex] is the angle
- O is the side opposite the angle
- A is the side adjacent the angle
From inspection of the triangle,
- [tex]x[/tex] = ∠X
- O = 77
- A = WX = 36
Substituting these values into the tan trig formula:
[tex]\implies \tan(X)=\dfrac{77}{36}[/tex]
Therefore, the tangent of ∠X is [tex]\dfrac{77}{36}[/tex]
