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lara31 [8.8K]
3 years ago
9

Georgia needed to sell her iPhone. She priced it at

Mathematics
1 answer:
nadezda [96]3 years ago
8 0

Answer:

572

Step-by-step explanation:

12% of 650 is 78

650 - 78 = 572

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Step-by-step explanation:

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point b on the ground is 5 cm from point E at the entrance to Ollie's house. He is 1.8 m tall and is standing at Point D, below
enot [183]

Point B on the ground is 5 cm from point E at the entrance to Ollie's house.

Ollie is at a distance of 2.45 m from the entrance to his house when he first activates the sensor.

The complete question is as follows:

Ollie has installed security lights on the side of his house that is activated by a  sensor. The sensor is located at point C directly above point D. The area covered by the sensor is shown by the shaded region enclosed by triangle ABC. The distance from A to B is 4.5 m, and the distance from B to C is 6m. Angle ACB is 15°.

The objective of this information is:

  • To find angle CAB and;
  • Find the distance Ollie is from the entrance to his house when he first activates the sensor.

The diagrammatic representation of the information given is shown in the image attached below.

Using  cosine rule to determine angle CAB, we have:

\mathbf{\dfrac{AB}{Sin \hat {ACB}} = \dfrac{BC}{Sin \hat {CAB}}= \dfrac{CA}{Sin \hat {ABC}}}

Here:

\mathbf{\dfrac{AB}{Sin \hat {ACB}} = \dfrac{BC}{Sin \hat {CAB}}}

\mathbf{\dfrac{4.5}{Sin \hat {15^0}} = \dfrac{6}{Sin \hat {CAB}}}

\mathbf{Sin \hat {CAB} = \dfrac{Sin 15 \times 6}{4.5}}

\mathbf{Sin \hat {CAB} = \dfrac{0.2588 \times 6}{4.5}}

\mathbf{Sin \hat {CAB} = 0.3451}

∠CAB = Sin⁻¹ (0.3451)

∠CAB = 20.19⁰

From the diagram attached;

  • assuming we have an imaginary position at the base of Ollie Standing point called point F when Ollie first activates the sensor;          

Then, we can say:

∠CBD = ∠GBF

∠GBF = (CAB + ACB)      

(because the exterior angles of a Δ is the sum of the two interior angles.

∠GBF = 15° + 20.19°

∠GBF = 35.19°

Using the trigonometric function for the tangent of an angle.

\mathbf{Tan \theta = \dfrac{GF}{BF}}

\mathbf{Tan \ 35.19  = \dfrac{1.8 \ m }{BF}}

\mathbf{BF  = \dfrac{1.8 \ m }{Tan \ 35.19}}

\mathbf{BF  = \dfrac{1.8 \ m }{0.7052}}

BF = 2.55 m

Finally, the distance of Ollie║FE║ from the entrance of his bouse is:

= 5 - 2.55 m

= 2.45 m

Therefore, we can conclude that Ollie is at a distance of 2.45 m from the entrance to his house when he first activates the sensor.

Learn more about exterior angles here:

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Wally purchased a desk that was on sale for 2/3 of the original price. If the original price was $450, what was the price that W
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Answer: wally paid $150 dollars for the desk.

Step-by-step explanation:

So if you do 450 divided by 3 you get 150. then you add 150 twice which gets you 300. then you subtract 450-300 and get 150.

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