The triangle WXY is a right-angle triangle, so the value of b is found out by the Pythagoras theorem.
The value of b is 9.37 or 9.4. Option D is the correct answer.
What is a Right-Angle Triangle?
A right-angle triangle can be defined as a triangle in which one angle is a right angle i.e. 90 degrees. In the right-angle triangle, the side opposite to the right angle is called the hypotenuse.
Given that [tex]\Delta WZX[/tex] is a triangle that is divided into two right-angle triangles [tex]\Delta WZY[/tex] and [tex]\Delta WYX[/tex].
In triangle WZY, [tex]\angle Y[/tex] is the right angle, and in triangle WYX, [tex]\angle Y[/tex] is the right angle.
In triangle ZWY,
[tex]tan \angle ZWY = \dfrac {ZY}{YW}[/tex]
[tex]tan \angle ZWY = \dfrac {5}{6}[/tex]......equation 1
In triangle WYX,
[tex]tan \angle WXY = \dfrac {WY}{XY}[/tex]
[tex]tan \angle WXY = \dfrac {6}{a}[/tex].........equation 2
Also in both triangles, [tex]\angle ZWY = \angle WXY[/tex]. then equation 1 = equation 2.
[tex]tan \angle ZWY = tan \angle WXY[/tex]
[tex]\dfrac {5}{6} = \dfrac {6}{a}[/tex]
[tex]5a=36[/tex]
[tex]a= 7.2[/tex]
In triangle WXY, the value of b is calculated by Pythagoras theorem,
[tex]WX^2 = WY^2+XY^2[/tex]
[tex]b^2 = 6^2 + a^2[/tex]
[tex]b^2 = 36 + (7.2)^2[/tex]
[tex]b = 9.37[/tex]
Hence we can conclude that the value of b is 9.37 or 9.4. Option D is the correct answer.
To know more about right-angle triangles, follow the link given below.
https://brainly.com/question/14796244.
