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asked Jan 14, 2020 104k views

1 Answer

Kemal Turk · Answer 1 · 2020-01-18T21:14:05+0000

The following are pairs of similar triangles:

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a. From
$\Delta OBA\sim\Delta OTE$ we have

$(OB)/(OT)=(OG)/(OE)\implies\frac{OB}4=(8.7)/(11.6)\implies OB=3$

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b.
$OT=OB+BT\implies4=3+BT\implies BT=1$

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c. From
$\Delta OBG\sim\Delta OTE$ we can find the length of BG:

$(BG)/(TE)=(OB)/(OT)\implies(BG)/(12)=\frac34\implies BG=9$

By the law of cosines, we can find the measure of angle BOG:

$BG^2=OB^2+OG^2-2OB\cdot OG\cos\angle BOG$

$9^2=3^2+8.7^2-2\cdot3\cdot8.7\cos\angle BOG$

$\implies m\angle BOG\approx85.95^\circ$

We use the law of sines to find the measure of angle OBG:

$(\sin\angle BOG)/(BG)=(\sin\angle OBG)/(OG)\implies m\angle OBG\approx74.63^\circ$

Finally,

$\sin\angle OBG=\frac{OA}3\implies OA\approx2.89$

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d.
$OU=OA+AU\implies OU\approx2.89+0.9\approx3.79$

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e.
$OE=OG+GE\implies11.6=8.7+GE\implies GE=2.9$

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f. See part c.
BG=9