Question

I really need help with this question!!

Answer 1

The following are pairs of similar triangles:

• OBN and OTS
• ONG and OSE
• OBG and OTE

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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`