A quicker way to find the area: At 4:07, Math Booster has found that BF = 4x/3. Apply the Pythagorean theorem to ΔBEF: (BF)² + (EF)² = 4², (4x/3)² + x² = 16, 16x²/9 + x² = 16, 16x² + 9x² = (9)(16), 25x² = 144 and x² = 144/25. The area of the square = x² = 144/25, as Math Booster also found.
The area is 144/25 units square. It has been a while since I haave had to learn that HL similarity would be applicable to theee ratios. Letter-wise the alpha angles are an inverse to the beta angles. And given that the letters of the alpha angles matches that of the triangles it now makes sense that there had to be theee ratios. I hope that I have made a good summary of this video.
It is lengthy solution. We have 3cos alpha = 4 sin alpha or tan alpha = 3/4. Hence, square side= 3 cos alpha = 3*4/5=12/5. Hence, square area = 12*12/25 =5.76.
Unnecessary to find AC and BC and then apply Pythagoras to the large triangle. You could have just applied it to one of the smaller triangle to find x^2.
A quicker way to find the area: At 4:07, Math Booster has found that BF = 4x/3. Apply the Pythagorean theorem to ΔBEF: (BF)² + (EF)² = 4², (4x/3)² + x² = 16, 16x²/9 + x² = 16, 16x² + 9x² = (9)(16), 25x² = 144 and x² = 144/25. The area of the square = x² = 144/25, as Math Booster also found.
Exactly. I did it on AED instead. It is unnecessary to find apply Pythagoras on the larger triangle.
EF= 4sinB
ED=3cosE
EF=ED( side of a square )
AngeB=AngleE
→ cosB=cosE
4SinB=3CosB
TanB=3/4
SinB=3/5
EF=3/5*4=12/5
Area =EF² = 144/25
The area is 144/25 units square. It has been a while since I haave had to learn that HL similarity would be applicable to theee ratios. Letter-wise the alpha angles are an inverse to the beta angles. And given that the letters of the alpha angles matches that of the triangles it now makes sense that there had to be theee ratios. I hope that I have made a good summary of this video.
It is lengthy solution. We have 3cos alpha = 4 sin alpha or tan alpha = 3/4. Hence, square side= 3 cos alpha = 3*4/5=12/5. Hence, square area = 12*12/25 =5.76.
love you voice +love how you solve maths
EF=x 4/x=3/AD AD=3x/4
ED=EF=x x^2+(3x/4)^2=3^2
25x^2/16=9
Area of square CDEF = x^2 = 144/25
cos a =x/3, sin a = a/4. Use cos^2 a+ sin^2 a = 1 to get 25x^2 = 144, so x^2 = 144/25. OLE.
9 minutes?
Unnecessary to find AC and BC and then apply Pythagoras to the large triangle. You could have just applied it to one of the smaller triangle to find x^2.
ED=a→ AD=3a/4 ; BF=4a/3 → (4+3)²=[(4a/3)+a]²+[a+(3a/4)]²→ a=12/5→ a²=144/25 ud².
Gracias y un saludo.
Use sin^2X+cos^2X=1 will be more simple.
arccos(l/3)+arccos(l/4)+90=180...l^2=144/25
Why's Alfa at triangles bottom and top same?
There is easier way.
Sin @ = x/4 Cos @ = x/3
Sin @^2 =x^2/16 Cos@^2 =x^2/9
X^2/16 + x^2/9 = 1
So x^2 = 144/25
sin α = s/4 ; cos α = s/3
tan α = (s/4)/(s/3) = 3/4
A = s² = (3 cosα)² = (4 sinα)²
A = 5,76 cm² ( Solved √ )
As tanB = 3/4, using Pythagorean triple 3-4-5, cosB = 4/5 and sinB = 3/5.
@@hongningsuen1348
Similarity of triangles:
s/3 = b/7 = 4/5 --> s=12/5
s² = 5,76 cm² ( Solved √ )
Similarity of triangles:
s/4 = h/7 = 3/5 --> s=12/5
s² = 5,76 cm² ( Solved √ )
Square area=(12/5)^2=144/25
It was enough:
x² + (4x/3)² = 4² (Pythagoras)
x² + 16x²/9=16
25x²=9×16→ *x²=144/25*
Que questão bonita. Parabéns pela escolha. Brasil - Outubro de 2024.
144/25
(3)^2 (4)^2={9+16}=25 180°ABC/25=7.5ABC (ABC ➖ 7ABC+5).
Let anyone method.Problem solving is nice and interesting.,🎉🎉🎉🎉🎉🎉🎉🎉🎉