The length of HI depends on the other lengths such as KI and LI, which
by Pythagorean theorem gives HI = 20.
Response:
Which relationship can be used to find the length of HI?
The given parameters are;
LH = 45
KH = 30
Required:
HI
According to Pythagorean theorem, we have;
KL = √(45² + 30²) = 15·√(13)
- [tex]\overline{KI}[/tex]² + [tex]\overline{KL}[/tex]² = (LH + HI)²
Which gives;
[tex]\overline{KI}[/tex]² + 15·√(13)² = (45 + HI)²
[tex]\mathbf{\overline{HI}}[/tex]² + [tex]\mathbf{\overline{KH}}[/tex]² = [tex]\overline{KI}[/tex]²
Which gives;
[tex]\overline{HI}[/tex]² + 30² = [tex]\mathbf{\overline{KI}}[/tex]²
[tex]\overline{HI}[/tex]² + 30² + (15·√(13))² = (45 + HI)² = 45² + 2×45×[tex]\overline{HI}[/tex] + [tex]\overline{HI}[/tex]²
30² + 15·√(13)² = 45² + 2×45×[tex]\overline{HI}[/tex]
2×45×[tex]\overline{HI}[/tex] = 30² + 15·√(13)² - 45² = 1800
[tex]\overline{HI} = \mathbf{\dfrac{1800}{2 \times 45} } = 20[/tex]
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