How to Find the Area of a Triangle Using Trigonometry

Math teacher John Schnatterly and I made a series of videos with the goal of "flipping" the classroom. They students watch the video and attempt the challenge question at home, and then do what would typically be homework in the classroom, where the teacher can help.
Check out our other videos in this series:
The Law of Sines: • The Law of Sines: How ...
How to find the length of an arc: • How to find the length...

[@amandabrown8100]

Thank you so much, you explained this so much better than my teacher, I finally understand it now. :)

[@TheHolyBaker]

Shout out to all my British people who use the metric system

[@Ushq_QgA]

why only British though😅

[@jarronjames107]

Everybody uses metric besides the US

[@evollove19]

The area for the last problem was 4.386 The angles for the bonus were 49.8 and the other two were 65.1

[@saphrosin2258]

do u think ur smart or something? all you gotta to do is remember the formula put it in your calculator and done, smh.

[@saphrosin2258]

shit's already mapped out for you as well

[@evollove19]

@@saphrosin2258 Not really. Ok, weird thing to point out. I wasn't disputing any of what you said.

[@saphrosin2258]

@@evollove19 +ratio

[@CatsAreAmazing8187]

@@saphrosin2258 to ratio someone you must get more likes than them!

[@kailibmendo9532]

you have saved me from failing my class thank youuuuu 😭

[@Lou-ry6yq]

I've solved your challenge question, it wasn't easy like I thought but here's how I did it: considering that the area and two of the sides of the triangle were given, I used heron's formula to determine the length of the last side, rearranging it into a 4th degree equation, which was very hairy but gave me the result of the last side, last side ≈ 10.10643 yds. Then I determined the measure of the angle opposite to the last side with the cosine rule, obtaining ≈ 49.81°, hence the measure of the corresponding angles is equivalent to: (180° - 49.81°) / 2 ; which is ≈ 65.1° To wrap it up, the angles are 65.1° ; 65.1° and 49.81° ; the last side is approximately 10.10643 yds. The method that I've use is pretty rough, but it works... I wish you told us how to solve it in an easier way!

[@fcar851]

IT is much easier to use the SAS formula for AREA ( A= 1/2 abSin C ) that he gave you in video ..Then solve for the angle Then subtract it from 180 and divide by 2 ...to get value of 2 same size angles ..as it is Isoceles TriangleThen see Emily answer in above comments.

[@bambiii787]

I went all my life until high school geometry not knowing it was bxh and not length x b for triangles

[@mathquizlet3177]

This video is a PowToon on LSD

[@fcar851]

Emily is close enough ..I think I got one angle 49.8 deg and two at 65.1 deg which adds up to 180 deg. ....as it is an isosceles triangle ..2 equal sides..2 equal angles

[@abbasyasin6851]

Could u explain how you got it

[@highfall8145]

its approximately 66 degrees for the equal side and 48 for the other one,

[@saur6270]

C=49.808 and A and B=65.096

[@minzu03]

thank you, this video was very nice to learn... :) but can we have the answer after the questions you gave us like the challenge question and the other question before?

[@maddolkar]

Are you alive

[@Abdalla7yousif]

@@maddolkarare you?.

[@sibomanatheogene6196]

Nice too

[@emilycornish1933]

I got C = 49.7 sq yards and A and B = 65.1 sq yards did anyone else get this? 😀

[@fcar851]

Emily is close enough ..see my answer in above comment

[@lettheworldwatch1124]

Well shit... My answer came out 3,999🤔

[@kelechio2653]

How is 12 the hypotenuse?

[@henryisonyoutube]

Because 12 is the opposite side of the right angle.

[@md.shahalamkhan335]

18 is the base and 12 is the hypotenuse which should be multiplied for finding area and divided by 2. He mainly explained about the h which is required for area of a triangle. After all he is right and perfect

[@yhwh8489]

@@henryisonyoutube actually this video didnt help me. I ended up doing the exact same thing in the video but in my problem I have to find the entire area etc pretty much the same but I didn't know that the hypotenuse is opposite of the right angle...well I did but forgot and I just wanna say *thanks so much*

[@tomgoodin5974]

12 is not the hypotenuse. A hypotenuse only exists in a right triangle. This is not a right triangle. It is only indicated that it is an isosceles triangle. We are informed that two sides are congruent and are 12 yards long. We don’t know the length of the base. If this were a right triangle and the 90° angle was between the 2 12 yard lengths, then the base would be the hypotenuse. This would be easier to solve the answer would be base times height divided by 2, or 12x12 / 2=72. Since the answer we are already given for the area is 55 yards we know that this is not a right triangle.

[@teknul89]

@@yhwh8489 ​I think it was very straightforward what he says You have a triangle but it’s not a right angle like this shape 📐 so he divided it up in to two pieces and focus on the right side of the triangle that one is an right angle shape You want to use sinus here because in your triangle you have only 37° and 12 which is the hypotenuse and you want to use the hight and there is (sinus, cosines and tangents) of those three you want to use sinus because you want to find the opposite side of the triangle which is Opposite / hypotenuse = Sinus So now you have sinus(37°) = h/12 And you want to multiply it with 12 on both sides so you get 12 sinus(37°) = h Use your calculator and rewrite sinus(37°) by using sin button and you should get 0,601815023152048 And now you have all your numbers and can now use them for your formula to solve the area which is Base * hight ------- = Area 2 18 * 12 * 0,601815023152048 ---------------- = 65 2 And you are done ✅ Remember you only found the area here and not the hight

[@myeducation6002]

I can suggest you to teach with paper...animation is very slow...

[@abdilaahihasan3406]

Answer of your chellenge question is→ -14.42

[@dragonblitz781]

why was it opp. and hyp. why not opp. and adj.

[@ZekTak]

Dragon Blitz because we don't know what adj is, we only know that it's a fraction of 18

[@teknul89]

@Dragon Blitz it’s because based on the triangle there was a value for hypotenuse and hight so the obvious one to use was the sinus

[@JoshPosn]

ily

[@anikadargata587]

you are mean!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

[@jonozzhang5087]

This is stupid just use Pythagorean theorem to find side B and that’s the height

[@dittode6307]

Don't you need a right triangle to use the Pythagorean Theorem? This will work with ANY triangle.

[@jonozzhang5087]

Dittode make a right triangle and find side b using Pythagorean theory to find the height

[@teknul89]

@@jonozzhang5087 ​You can not use Pythagoras theorem when it’s the area of the triangle you want to find And if you followed the video you would also know that he said we have not found the hight but the area of the triangle

[@sibomanatheogene6196]

Nice too