Answer:
[tex]a=5\frac{1}{3}[/tex] is the answer.
Step-by-step explanation:
In the given triangle YWZ
WZ² = YW² + YZ²
c² = 4² + 3² = 16 + 9 = 25
c = 5
In the ΔXYW
b² = 4² + a²-----(1)
In the right angle triangle WXZ
(a + 3)² = b² + c²
a² + 9 + 6a = b²+ c²
By putting value of b² from equation 1.
a² + 9 + 6a = 16 + a² + 25
6a + 9 = 41
6a = 41 - 9
6a = 32
a = 32/6 = 16/3
[tex]a=5\frac{1}{3}[/tex]
So [tex]a=5\frac{1}{3}[/tex] is the answer.
