Question

Thx and have a great day!!

Answer 1

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

$\sin (\angle TRU)= \frac{\textrm{side opposite to angle TRU}}{Hypotenuse} \\\\\\and\\\sin (\angle IRU)= \frac{\textrm{side opposite to angle IRU}}{Hypotenuse}$

Now,

∠ TRU = ∠ IRU = 19° ............Given

Substituting the given values in it we get

$\sin 19=\frac{2x+5}{RU} \\and\\\sin 19=\frac{7x}{RU} \\\textrm{on equating both the equation we get}\\\\7x=2x+5\\7x-2x=5\\\\5x=5\\\\x=\frac{5}{5} \\\\x=1$

Therefore,

IU = 7x = 7×1 = 7 units