Related Rates - Area of a Triangle

This calculus video tutorial explains how to solve related rate problems dealing with the area of a triangle. The first problem asks you to find the rate at which the area of a right triangle is changing. You need to use the product rule using the rates at which the base and height of the right triangle are changing. The second problem asks you to find the rate at which the area of a triangle is changing using the area formula with sines.

Related Rates - Free Formula Sheet:

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Introduction to Limits:

Derivatives - Fast Review:

Introduction to Related Rates:

Derivative Notations:

Related Rates - The Cube:

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Inflated Balloon & Melting Snowball:

Gravel Dumped Into Conical Tank:

Related Rates - Area of a Triangle:

Related Rates - The Ladder Problem:

Related Rates - The Distance Problem:

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Related Rates - Airplane Problems:

Related Rates - The Shadow Problem:

Related Rates - The Baseball Diamond Problem:

Related Rates - The Angle of Elevation Problem:

Related Rates - More Practice Problems:

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Final Exams and Video Playlists:

Full-Length Videos and Worksheets:

[georgesadler]

MR. Organic Chemistry Tutor, thank you for another short and sweet video/lecture on Related Rates in Calculus One. This is an error free video/lecture on YouTube TV with the Organic Chemistry Tutor.

[cariboux]

Brilliant! Even a dummy like I can understand this. I love your rigorous methodology. It's something even Khan doesn't always stick to. Thank you!

[puddingmachatea]

You are always so calm and watching your video also calm down my heart, appreciated your work

[joerohle]

holy shit i understand what’s happening now. thank you

[aerisoraerith]

thank you so much, i had no idea it was this simple

[sergiovalencia]

After one minute, you have the triangle, 11x15. The gain in area is 42.5cm2.

[sjsnnsndxdnendnndd]

Any ocr mei dudes tryna predict the qs

[mustafamalik]

Don't you mean he's quite amazing

[adegboyegasamuel]

Two sides of a triangle have length 3m and 1m. The angle between them is decreasing at the rate of 1°/min. How fast is the length of the third side changing when the angle between the two other sides of fixed length is 60° ? (Do Not Simplify Your Answer) (Hint: Recall the cosine rule: a² = b² + c2 - 2bc cos 0 )

I tried to follow the process I'm not getting this

Pls I need help on this

[timpitkin]

In example 1, shouldn't the function read dA/dt =1/2 (dh/dt)(h) + 1/2 (db/dt)(b)?

[ticciblaze]

you're real quiet...even at full volume.

[DonClavaton]

Can somebody tell me why cos pi/3 is equals to 1/2

[BiggStink]

For the second example with the increasing angle, when the angle is PI radians, the area would be zero wouldn't it? (flat triangle)
That would happen after PI / 0.15 minutes.

But the final answer says the area at that time would be 1.5 * (PI/0.15mins) m^2. Which isn't zero?

Can someone help me understand this? Thanks

[nataliaandrade]

How are both the base and the height increasing? If one increases, shouldn't the other decrease?