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Aliaa and Zhang Li are tennis-playing robots capable of placing shots with superhuman precision
thagore
Aliaa is about to hit its next shot to the far corner of the court. It (Aliaa) knows that the distance between
itself and Zhang Li is 520 cm, and it knows that the angle between Zhang Li and the far corner is 53°
Similarly, Zhang Li knows that the angle between Aliaa and the far corner is 100°.
ythagore
What distance should Aliaa hit the ball so that it lands perfectly in the far corner of the court?
Do not round during your calculations. Round your final answer to the nearest centimeter.
pecialrig
cm
100% 150
Aliaa
TV53°
520 cm
Introductie
100
Zhang Li
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Answer 1

1128cm

Explanation:

The diagram of the problem is annotated and attached.

In the diagram, we are required to find the distance between Aliaa and the far corner, b.

In Triangle ABC

`\angle A+\angle B+\angle C=180^\circ\\53^\circ+100^\circ+\angle C=180^\circ\\\angle C=180^\circ-153^\circ\\\angle C=27^\circ`

Using Law of Sines

`(b)/(sin B) =(c)/(sin C) \\(b)/(sin 100) =(520)/(sin 27)\\b=(520 X sin 100)/ sin 27\\b=1127.997\\b\approx 1128$ cm (to the nearest centimeter.)`

Therefore, Aliaa should hit the ball a distance of 1128cm so that it lands perfectly in the far corner of the court.