Can you find angle X? | Area of the Blue Shaded triangle is 6

Can you find angle X? | Area of the Blue Shaded triangle is 6 | Important Geometry skills explained

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Жыл бұрын

Learn how to find the angle X in the blue shaded triangle. Important Geometry skills are also explained: area of the triangle formula; Trigonometry; Pythagorean theorem. Step-by-step tutorial by PreMath.com
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Can you find angle X? | Area of the Blue Shaded triangle is 6 | Important Geometry skills explained
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Пікірлер: 55

@misterenter-iz7rz Жыл бұрын

First impression : very difficult😢.

@PreMath Жыл бұрын

Thanks for your feedback! Cheers! 😀

@ybodoN Жыл бұрын

Once we have found BC = 6 and AB = BE = 10, we also know that CE = 8. So x = arctan 10/6 − arctan 8/6 ≈ 5.91° If we use use trigonometric identities to get an exact value: tan x = (10/6 − 8/6) / (1 + 10/6 ⋅ 8/6) ⇒ tan x = 3/29

@harikatragadda Жыл бұрын

TanX = Tan(∠DBC - ∠EBC) = (DC/BC - EC/BC)/{1+(DC*EC/BC*BC)}= 3/29

@math-problem6940 Жыл бұрын

Without using area of blue triangle...we can also find angle x by using the law of cosine. Thanks for your problem. I always follow your newest math problem. Warm regards from Indonesia.

@williamwingo4740 Жыл бұрын

I got 5.906 degrees: Invoking Pythagoras, I got the dimensions of the rectangle as 6x10 by a slight variation on your method; but I'll skip the details. Then angle x = angle ABE -- angle ABD. Tan ABE = 6/8 = 0.75; and tan ABD = 6/10 = 0.60. So angle x = arctan(0.75) -- arctan(0.60) = 36.8699 -- 30.9637 = 5.906 degrees. Cheers. 🤠

@Abby-hi4sf Жыл бұрын

Keep up the great page! I am number one fun!

@PreMath Жыл бұрын

Thanks! Will do! Take care dear

@jimlocke9320 Жыл бұрын

We note that

@user-mr9ce4os2s Жыл бұрын

Impressed, all you need is just to focus a little bit.

@mega_mango Жыл бұрын

U have very kind community, pre math. I love it =)

@PreMath Жыл бұрын

I'm very blessed. So nice of you. Thank you! Cheers! 😀

@murdock5537 11 ай бұрын

Nice and awesome, many thanks! AB = BE = y area ∆BED = 6 = gh/2 = 2h/2 = h = AD → sin⁡(δ) = (y - 2)/y → cos⁡(δ) = 6/y → sin^2(δ) + cos^2(δ) = 1 → 4y = 40 → y = 10 → y - 2 = 8 → BD = √136 = 2√34 → 6 = (1/2)10(2√34)sin⁡(φ) → sin⁡(φ) = 3√34/170 → φ ≈ 5,9° or: tan⁡(θ) = 3/5; tan⁡(τ) = cot⁡(θ) = 5/3; tan⁡(δ) = 4/3 → tan⁡(τ - δ) = (tan⁡(τ) - tan⁡(δ))/(1 + tan⁡(τ)tan⁡(δ)) = 3/29 → τ - δ = φ ≈ 5,9°

@PreMath 11 ай бұрын

Excellent! Thank you! Cheers! 😀

@parthtomar6987 11 ай бұрын

Nice sir🎉

@samrudhb7855 11 ай бұрын

Awesome question 😅

@MrPaulc222 Жыл бұрын

Good explanation. I did the final part with

@PreMath Жыл бұрын

Thank you! Cheers! 😀

@user-sw9lb2zs6e 21 күн бұрын

Quicker Solution at the end: 6 and 10 are my lengths for tan BETA , 6 and 8 are side lengths for tan E , angle sum in the two triangles 180 , 90 degrees- 53,1 degrees- 30,96 degrees = 5,93 degrees

@wackojacko3962 Жыл бұрын

What is the Gaussian Radius of these square units? Just asking for a friend......never mind, I answered my own question . Constant Zero Gaussian surfaces!.... and that's when the study of Euclidean geometry becomes so much fun with you Sir. 🙂

@HappyFamilyOnline Жыл бұрын

Very well explained 👍 Thanks for sharing😊

@PreMath Жыл бұрын

Thanks for liking

@KAvi_YA666 Жыл бұрын

Thanks for video.Good luck sir!!!!!!!

@PreMath Жыл бұрын

Thank you too

@Copernicusfreud Жыл бұрын

Yay! I solved it.

@PreMath Жыл бұрын

Awesome!

@montynorth3009 Жыл бұрын

Using Trig. as alternative once length y was calculated. Tan EBC = 8/6, EBC = 53.13 degrees. Tan ABD = 6/10, ABD = 30.96 degrees. Then x = 90 - 53.13 - 30.96 = 5.91 degrees.

@vidyadharjoshi5714 Жыл бұрын

0.5*AD*DE = 6. AD = 6. Let AB = A. Asq = 36 + (A-2)sq. A = 10. Angle X = InvTan (6/8) - InvTan (6/10) = 5.9 Deg.

@theoyanto Жыл бұрын

Yeah, maybe I'm not on form or just plain dumb, didn't manage this on but still got much enjoyment from it. Thank you.

@PreMath Жыл бұрын

You are very welcome! Thank you! Cheers! 😀

@rishudubey1533 Жыл бұрын

thankyou so much dear ❤❤

@PreMath Жыл бұрын

You are so welcome! So nice of you, dear Thank you! Cheers! 😀

@24_tranlamanhkhoa61 Жыл бұрын

I find it quite ez… the key here is to find the length of AD, then just use equation… very ezzzz…

@misterenter-iz7rz Жыл бұрын

6:30 PM in HK, very early in USA 😮

@PreMath Жыл бұрын

Very true! It's 3:30 AM here in the USA. Take care. Thank you! Cheers! 😀

@marioalb9726 Жыл бұрын

Area of blue triangle with b=2 : A = ½ b. h = ½ 2 h = 6 cm² h = 6 cm Side EB = base of rectangle b² = (b-2)²+h² b² = (b² -4b + 4) + h² 4b = h² + 4 b = h²/4 + 1 = 6²/4+1 b = 10 cm x = α - β tan α = 10/6 , α = 59,04° tan β = 8/6 , β = 53,13° x = 5,906° ( Solved √ )

@giuseppemalaguti435 Жыл бұрын

x=arctg3/29

@AfricAndroidTraining Ай бұрын

Great explanation! It seems like h is not part of the triangle DBE. But why did you use h as Height in this : 6 = 1/2(2)(h) ?

@harrymatabal8448 28 күн бұрын

Mr African, good question. I was also puzzled. But if you look again at the blue triangle the base is 2. Now think again about the height. It does not have to be inside the triangle. Any perpendicular distance from the opposite sides will be the height.

@misterenter-iz7rz Жыл бұрын

By the foolish way, let axb be the dimension of the rectangle, so BD^2=a^2+b^2, BE^2=b^2=a^2+(b-2)^2, so a^2=4b-4, and 144=(a^2+b^2)b^2sin^2 x=(b^2+4b-4)b^2sin^2 x, 4=b^2+(b^2+4b-4)-2b sqrt(b^2+4b-4)cos x, it becomes very clumsy to solve for x and b from these two equations 😅

@goldenbeastsilver6728 Жыл бұрын

Why is the answer wrong when i use trig ratios to get the side length DB?

@lk-wr2yn 6 ай бұрын

Tan-1(6÷10)-Tan-1(8÷10)

@comdo777 Жыл бұрын

as n were=25 os is it

@pralhadraochavan5179 Жыл бұрын

Good night sir

@PreMath Жыл бұрын

Same to you, dear

@soli9mana-soli4953 Жыл бұрын

Me 5,91°

@jumin5419 Жыл бұрын

Why DE is a base of triangle not DB? and height triangle DEB why took DA...DA is height of triangle DAB

@thewolfdoctor761 Жыл бұрын

Because initially we know the value of DE to be 2 but we don't know the value of DB, while the area is given as 6.

@bigm383 Жыл бұрын

❤🥂👍😀

@PreMath Жыл бұрын

So nice of you. Thank you! Cheers! 😀

@-HoQuynhTrangA 11 ай бұрын

so difficult 🥲🥲🥲🥲

@ernestschoenmakers8181 Жыл бұрын

It's better to call the unknown angle alpha.

@PreMath Жыл бұрын

Thank you! Cheers! 😀

@ybodoN Жыл бұрын

I use alpha for a first angle (followed by beta, gamma, delta). Where there is only one unknown angle, I prefer to use theta. But the Greek letter chi (Χ or χ) could also be a valid option...

@marioalb9726 Жыл бұрын

Area of blue triangle : b=2cm A = ½ b. h = 6 cm² A = ½ 2 h h = 6 cm Side EB = base of rectangle b² = (b-2)²+h² b² = (b² -4b + 4) + h² 4b = h² + 4 b = h²/4 + 1 = 6²/4+1 b = 10 cm Area of blue triangle: A = ½ b.d sinx sin x = 2A/(b.d) sin x = 2A/(b.√(b²+h²)) sin x = 2.6/(10√(10²+6²)) sin x = 12 /(10.11,66) sin x = 0,1029 x = 5,906° ( Solved √ )