Ace school

with brainly

  • Get help from millions of students
  • Learn from experts with step-by-step explanations
  • Level-up by helping others

A community for students.

In the quadrilateral sketch opposite,

Mathematics
See more answers at brainly.com
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Join Brainly to access

this expert answer

SIGN UP FOR FREE
|dw:1367567372412:dw|
|dw:1367568505062:dw|
first, look at triangle ABC and triangle ACD AC^2 (triangle ABC) = AC^2 (triangle ACD) (3x)^2 + x^2 = y^2 + (2y)^2 10x^2 = 5y^2 y^2 = 2x^2 ... (1) we knowed that :

Not the answer you are looking for?

Search for more explanations.

Ask your own question

Other answers:

now, look at the triangle of BCD by using cosine rule, we have : BD^2 = BC^2 + CD^2 - 2 BC CD cos
also, look at the triangle of ABD by using cosine rule, we have : BD^2 = AB^2 + AD^2 - 2 AB AD cosA BD^2 = (3x)^2 + (2y)^2 - 2 (3x) (2y) cosA BD^2 = 9x^2 + 4y^2 - 12xy cosA because y^2 = 2x^2 ---->y = x sqrt(2) then the equation above can be BD^2 = 9x^2 + 4(2x^2) -12x(x sqrt(2))cosA BD^2 = 9x^2 + 8x^2 -12x^2 sqrt(2)cosA BD^2 = 17x^2 - 12x^2 * sqrt(2)cosA
now, campare the values of both (BD^2) BD^2 = 3x^2 + 2 xycosA and BD^2 = 17x^2 - 12x^2 * sqrt(2)cosA it means : 17x^2 - 12x^2 * sqrt(2)cosA = 3x^2 + 2 xycosA combine the similar terms, giving us 17x^2 - 3x^2 = 2 xycosA + 12x^2 * sqrt(2)cosA 14x^2 = 2 xycosA + 12x^2 * sqrt(2)cosA
opps.. the value of y above must subtituted be x sqrt(2) so, we have : 14x^2 = 2 xycosA + 12x^2 * sqrt(2)cosA 14x^2 = 2 x(x sqrt(2))cosA + 12x^2 * sqrt(2)cosA 14x^2 = 2x^2 sqrt(2)cosA + 12x^2 * sqrt(2)cosA 14x^2 = 14x^2 sqrt(2) cosA divide by 14x^2 to both sides, becomes 1 = sqrt(2) cosA
then finally, 1 = sqrt(2) cosA or cosA = 1/sqrt(2) = 1/2 * sqrt(2) A = 45 degrees QED :)
thanks so MUCH!!!
you're welcome :)

Not the answer you are looking for?

Search for more explanations.

Ask your own question