Question

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Answer 1

Therefore,

IU = 7x = 7×1 = 7 units

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=(2x+5)/(RU) \\and\\\sin 19=(7x)/(RU) \\\textrm{on equating both the equation we get}\\\\7x=2x+5\\7x-2x=5\\\\5x=5\\\\x=(5)/(5) \\\\x=1`

Therefore,

IU = 7x = 7×1 = 7 units