From the Δ YWZ we get c = 5 then the value of [tex]$a= 5 \frac{1}{3}[/tex].
In the given Δ YWZ
WZ² = YW² + YZ²
c² = 4² + 3² = 16 + 9 = 25
c = 5
In the Δ XYW
b² = 4² + a²-----(1)
In the right-angle Δ WXZ
(a + 3)² = b² + c²
a² + 9 + 6a = b²+ c²
By putting the value of b² from (1)
a² + 9 + 6a = 16 + a² + 25
Simplifying the above equation, we get
6a + 9 = 41
6a = 41 - 9
6a = 32
[tex]$a = \frac{32}{6} = \frac{16}{3}[/tex]
[tex]$a= 5 \frac{1}{3}[/tex]
Therefore, the value of [tex]$a= 5 \frac{1}{3}[/tex].
To learn more about the value of a refer to:
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