The value of x in the given diagram is 7cm.
What is tangent of an angle?
The tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side.
According to the given question.
We have a diagram in which we have two right angled triangles.
Now, in the upper right angled triangle
[tex]tan50 = \frac{0pposite side}{5}[/tex]
⇒ 1.19 = 0pposite side/ 5
⇒ opposite side = 1.19 × 5
⇒ opposite side = 1.2 × 5
⇒ opposite side = 6cm
Now, the opposite side w.r.t angle 50 degrees in the upper right angle triangle is a adjacent side w.r.t to angle 38 degrees in the lower right angle triangle.
So, in the lower right angle triangle.
[tex]tan38 = \frac{x}{adjacent side}[/tex]
⇒[tex]0.78 = \frac{x}{6}[/tex]
⇒ x = 0.78 × 6
⇒ x = 4.68
⇒ x = 7cm
Hence, the value of x in the given diagram is 7cm.
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