AB and DE are chords that intersect at point F inside circle C as shown. If the measure of arc EA

Mathematics

1 answer:

barxatty [35]4 years ago

4 0

Answer:

Do you have an image of the circle? I might be able to help with that.

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Your lunch bill is $19.75. A 5% sales tax will be added, and you want to give a tip of about 20% of $19.75. Estimate how much yo

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Total $19.75
Adding 5%
Taking away 20%

1). $19.75 x 0.20(20%) = 3.95
3.95 + 19.75 = 23.7

2). $19.75 x 0.05(5%) = 0.9875
0.9875 + 23.7 = 24.6875

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A small plane and a large plane are 6.8km from each other, at the same altitude (height). From an observation tower, the two air

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Answer:

7.9km

Step-by-step explanation:

(a)See attached for the diagram representing this situation.

(b)

In Triangle ABC

$\text{Using Law of Sines}\\\dfrac{\sin A}{a}=\dfrac{\sin C}{c} \\\dfrac{\sin A}{5.2}=\dfrac{\sin 58^\circ}{6.8} \\\sin A=5.2 \times \dfrac{\sin 58^\circ}{6.8}\\A=\arcsin (5.2 \times \dfrac{\sin 58^\circ}{6.8})\\A=40.43^\circ$

Next, we determine the value of Angle B.

$\angle A+\angle B+\angle C=180^\circ\\40.43+58+\angle B=180^\circ\\\angle B=180^\circ-(40.43+58)\\\angle B=81.57^\circ$

Finally, we find b.

$\text{Using Law of SInes}\\\dfrac{b}{\sin B}=\dfrac{c}{\sin C} \\\dfrac{b}{\sin 81.57^\circ}=\dfrac{6.8}{\sin 58^\circ} \\b=\dfrac{6.8}{\sin 58^\circ} \times \sin 81.57^\circ\\b=7.9km $ (to the nearest tenth of a kilometer)$

The distance between the small plane and the observation tower is 7.9km.

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