Question

$\huge\red{Question}$

A housefly is sitting on top of the lamp and was looking at the dustbin which was 20m high. the angle of depression from the top and the bottom of the dustbin from the housefly position where 30° and 45° respectively.


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Answer 1

Answer:

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Step-by-step explanation:

The warm weather brings unwanted guests with it every summer. Flies come back into your kitchen and lay eggs in the dustbin, which then hatch, causing you to have even more flies in your home.

These tips will hopefully help you to chase away the flies that are hiding in your rubbish bins or in your home.

Clean your garbage cans regularly with soap and water and keep the kitchen clean. Do not leave leftovers out in trays or pans that have not been washed, and throw away empty beverage bottles or cartons immediately.

2. Keep Your Dustbin Dry

There are biodegradable waste bags that you can use instead of ordinary plastic bags. Moisture from the waste can evaporate from the food, but it gets trapped inside plastic waste bags. In biodegradable ones, the waste dries out, decreasing the risk of attracting flies. The trash can also stays cleaner.

You can also put newspapers at the bottom of the dustbin to help absorb moisture. A dry trash can also attracts less of other insects.

Fruit flies are attracted to rotting fruit, to make sure all the fruit in your fruit basket is fresh and clean.

Fruit flies are attracted to rotting fruit, to make sure all the fruit in your fruit basket is fresh and clean.

skeeze

3. Keep Small Flies Away From Your Fruit Basket

If you have a fruit bowl, check often to make sure that the fruit inside is still fresh. If you place new fruit in it, wash them first. Fruit that is rotten or overripe will attract fruit flies. Fruit flies are annoying little flies and they come in dozens. Getting rid of them is even more annoying because they're small and hard to see.

4. Use Vinegar to Clean

When you clean the stove and hotplates in your kitchen, use a few drops of vinegar. The smell of vinegar chases flies away. Clean your stove regularly. This also increases the lifespan of your furnace.

5. Place the Dustbin Outside of the Kitchen

If you have space, then put the trash can outside of the kitchen—in the laundry room, for example. That way, flies won't come into your kitchen anymore.

If you have a wheelie bin in the garage, then leave the lid closed. If it's in the garden under the sun, you could leave it about an inch open to let the waste breath and dry out. Waste that is dry attracts fewer pests.

Answer 2

Correct Question:

$\textsf{ A housefly is sitting on top of the lamp and was} \\ \textsf{looking at the dustbin which was 20 m high} \\ \sf{the \ angle \ of \ depression \ to \ the \ top \ and} \\ \sf{and \ the \ bottom \ of \ the \ dustbin \ from \ the} \\ \sf{housefly \ position \ were \ 30^\circ \ and \ 45^\circ \ respectively.} \\ \sf{Find \ the \ height \ of \ the \ lamp. }$

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Answer:

$\sf{The \ height \ of \ the \ lamp \ is \ (30+10\sqrt3) \ m}$

Given:

$\sf{\leadsto{Height \ of \ dustbin \ is \ 20 \ m}} \\ \sf{\leadsto{Angle \ of \ depression \ to \ the \ top \ and \ bottom}} \\ \sf{of \ dustbin \ were \ 30^\circ \ and \ 45^\circ \ respectively. }$

To find:

$\sf{The \ height \ of \ the \ lamp.}$

Solution:

$\sf{Let \ seg \ EB \ represent \ the \ lamp \ and} \\ \sf{seg \ DC \ represent \ the \ dustbin.}$

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Construction:

$\sf{Draw \ seg \ AD \ perpendicular \ to \ seg \ DC}$

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$\sf{\angle EDA = 30^\circ \ and \ \angle ECB=45^\circ} \\ \\ \sf{...[Alternate \ angles]} \\ \\ \sf{In \ quadrilateral \ ABCD,} \\ \\ \sf{\angle ABC=90^\circ} \\ \\ \sf{\angle DCB=90^\circ,} \\ \\ \sf{\angle BAD=90^\circ...construction,} \\ \\ \sf{\angle ADC=90^\circ...remaining \ angle} \\ \\ \sf{\therefore{Quadrilateral \ ABCD \ is \ a \ rectangle}} \\ \\ \sf{By \ the \ property \ of \ rectangle}$

$\sf{Let \ AE=x} \\ \\ \sf{In \ \triangle EAD,} \\ \\ \sf{\angle EDA=30^\circ} \\ \\ \sf{tan\theta=\dfrac{AE}{AD}} \\ \\ \sf{\therefore{tan30^\circ=\dfrac{x}{AD}}} \\ \\ \sf{\therefore{\dfrac{1}{\sqrt3}=\dfrac{x}{AD}}} \\ \\ \sf{\therefore{AD=\sqrt3x}}$

$\sf{AB=DC=20 \ m \ and \ BC = AD=\sqrt3x} \\ \\ \sf{In \ \triangle \ EBC,} \\ \\ \sf{AB=20 \ m \ and \ \angle ECB=45^\circ} \\ \\ \sf{tan\theta=\dfrac{EB}{BC}} \\ \\ \sf{\therefore{tan45^\circ=\dfrac{AE+AB}{BC}}} \\ \\ \sf{But, \ tan45^\circ=1 \ and \ AE=x \ and \ AB=20} \\ \\ \sf{\therefore{\dfrac{x+20}{\sqrt3}=1}} \\ \\ \sf{\therefore{\sqrt3x=x+20}} \\ \\ \sf{On \ squaring \ we \ get,} \\ \\ \sf{3x^{2}=x^{2}+400+40x} \\ \\ \sf{2x^{2}-400-40x=0} \\ \\ \sf{\therefore{x=\dfrac{-b\pm\sqrt{b^{2}-4ac}}{2a}}} \\ \\ \sf{But, \ height \ is \ always \ positive. } \\ \\ \sf{x=\dfrac{20+\sqrt{400+800}}{2}} \\ \\ \sf{x=\dfrac{20+20\sqrt3}{2}} \\ \\ \sf{\therefore{x=10+10\sqrt3}} \\ \\ \sf{\therefore{AE=10+10\sqrt3}}$

$\sf{Height \ of \ the \ lamp=AB+AE}$

$\sf{\therefore{Height \ of \ the \ lamp=20+10+10\sqrt3}} \\ \\ \sf{\therefore{Height \ of \ the \ lamp=(30+10\sqrt3) \ m}} \\ \\ \purple{\tt{\therefore{Height \ of \ the \ lamp=(30+10\sqrt3) \ m}}}$