Answer:
Therefore,
IU = 7x = 7×1 = 7 units
Step-by-step explanation:
Given:
Δ TRU and Δ IRU are right angle triangle.
TU = 2x + 5
IU = 7x
RU = common Hypotenuse
To Find:
IU = ?
Solution:
In right angle triangles Δ TRU and Δ IRU we have sine identity as
[tex]\sin (\angle TRU)= \frac{\textrm{side opposite to angle TRU}}{Hypotenuse} \\\\\\and\\\sin (\angle IRU)= \frac{\textrm{side opposite to angle IRU}}{Hypotenuse}[/tex]
Now,
∠ TRU = ∠ IRU = 19° ............Given
Substituting the given values in it we get
[tex]\sin 19=\frac{2x+5}{RU} \\and\\\sin 19=\frac{7x}{RU} \\\textrm{on equating both the equation we get}\\\\7x=2x+5\\7x-2x=5\\\\5x=5\\\\x=\frac{5}{5} \\\\x=1[/tex]
Therefore,
IU = 7x = 7×1 = 7 units
