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morpeh [17]
2 years ago
15

Consider in the figure below.

Mathematics
2 answers:
ELEN [110]2 years ago
6 0

⚘ <em>R</em><em>e</em><em>f</em><em>e</em><em>r</em><em> </em><em>t</em><em>o</em><em> </em><em>t</em><em>h</em><em>e</em><em> </em><em>a</em><em>t</em><em>t</em><em>a</em><em>c</em><em>h</em><em>m</em><em>e</em><em>n</em><em>t</em><em>s</em><em>!</em><em>!</em><em>~</em>

marusya05 [52]2 years ago
5 0

Let's solve

in ∆GNK

  • GN=130
  • GJ=94
  • GK=GJ/2=47

Apply pythagorean theorem

\\ \sf\longmapsto NK^2=GN^2-GK^2=130^2-47^2=16900-2209=14691

\\ \sf\longmapsto NK=\sqrt{14691}

\\ \sf\longmapsto NK=121(Approx)

If you observe the traingle

  • GN=NJ=130

\\ \sf\longmapsto LJ^2=JN^2-LN^2

\\ \sf\longmapsto LJ^2=130^2-78^2

\\ \sf\longmapsto LJ^2=16900-6084

\\ \sf\longmapsto LJ^2=10816

\\ \sf\longmapsto LJ=\sqrt{10816}

\\ \sf\longmapsto LJ=104

  • LH=LJ =104

So

in ∆HNL

\\ \sf\longmapsto HN^2=104^2+78^2

\\ \sf\longmapsto HN^2=10816+6084

\\ \sf\longmapsto HN^2=16900

\\ \sf\longmapsto HN=\sqrt{16900}

\\ \sf\longmapsto HN=130

Done .

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