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safia21
 3 years ago
−
Calculate the length of LM in the isosceles right triangle ∆ KLM
safia21
 3 years ago
− Calculate the length of LM in the isosceles right triangle ∆ KLM

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heisenberg
 3 years ago
Best ResponseYou've already chosen the best response.2You can use the pythagorean theorem since it has a right angle. Are you familiar with it?

heisenberg
 3 years ago
Best ResponseYou've already chosen the best response.2do you know what a hypotenuse is?

heisenberg
 3 years ago
Best ResponseYou've already chosen the best response.2so the pythagorean theorem is: \[ a^2 + b^2 = c^2 \] where c is the hypotenuse. since this is an isosceles triangle, a = b, don't you think?

heisenberg
 3 years ago
Best ResponseYou've already chosen the best response.2so can you take it form here? since a = b, \( a^2 + a^2 = c^2 \)

safia21
 3 years ago
Best ResponseYou've already chosen the best response.1what is a and what is like what do you plug in

heisenberg
 3 years ago
Best ResponseYou've already chosen the best response.2well let me ask, what is a hypotenuse?

safia21
 3 years ago
Best ResponseYou've already chosen the best response.1the longset side of a right triangle

heisenberg
 3 years ago
Best ResponseYou've already chosen the best response.2very good! which is the side *directly* across from the right angle. so the other two sides would be 'a' and 'b', but this triangle is isosceles so a = b. therefore a is an unknown that we want to solve for and 'c' is the length of the hypotenuse

heisenberg
 3 years ago
Best ResponseYou've already chosen the best response.2so if we have \(a^2 + a^2 = c^2\) where \( c = 36 \) we only have 1 unknown so we should be able to solve this like a regular algebra problem.

heisenberg
 3 years ago
Best ResponseYou've already chosen the best response.2are you still confused? all that's left is to simplify this equation and solve.

heisenberg
 3 years ago
Best ResponseYou've already chosen the best response.2show me your steps. i don't that's right.

heisenberg
 3 years ago
Best ResponseYou've already chosen the best response.2what is \( a^2 + a^2 \) ?

heisenberg
 3 years ago
Best ResponseYou've already chosen the best response.2(@victor, please consider that the best way for a person to learn something is to have the person discover it on their own rather than just giving that person an answer.)

heisenberg
 3 years ago
Best ResponseYou've already chosen the best response.2there's no reason you can't do it yourself, though. you have an equation. where are you getting stuck? show me your work and i can help you.

safia21
 3 years ago
Best ResponseYou've already chosen the best response.1can we start from the beginning im soo sorry!

heisenberg
 3 years ago
Best ResponseYou've already chosen the best response.2the pythagorean theorem states that (for a right triangle): \[ a^2 + b^2 = c^2\]where c is the hypotenuse. we have the hypotenuse in this case, as you pointed out, and it equals 36, agree?

Victor_Hugo
 3 years ago
Best ResponseYou've already chosen the best response.0It's an isosceles triangle so it has two equal sides and therefor two equal angles. If you add the inner angles of any triangle the result will be 180º. You already know 1 angle = 90º. 18090=90 And since the two other angles are equal you have 90/2=45. Now that you have all the angles you can use trigonometry and achieve the value of the sides. I recommend you use "sin" or "tan" (as expressed on a calculator).

heisenberg
 3 years ago
Best ResponseYou've already chosen the best response.2but this is an isosceles triangle, so the two remaining sides are equal in length, would you agree?

Victor_Hugo
 3 years ago
Best ResponseYou've already chosen the best response.0Of course, you only need the value of one side.

heisenberg
 3 years ago
Best ResponseYou've already chosen the best response.2so since the two remaining sides are \(a\) and \(b\), we know that \(a =b \) therefore we can simplify the equation to this: \( a^2 + a^2 = c^2 \)

safia21
 3 years ago
Best ResponseYou've already chosen the best response.1okay and c2 is 36 right so a2+a2= 36^2

heisenberg
 3 years ago
Best ResponseYou've already chosen the best response.2exactly! so what does \( a^2 + a^2\) equal? we can reduce this to one term.

heisenberg
 3 years ago
Best ResponseYou've already chosen the best response.2not quite. how about this, what does \( x + x \) equal?

heisenberg
 3 years ago
Best ResponseYou've already chosen the best response.2what if i wrote it this way: \( 1x+ 1x \)

heisenberg
 3 years ago
Best ResponseYou've already chosen the best response.2that wouldn't work. think about if x = 2, 1x + 1x = 1(2) + 1(2) = 4, but 2x^2 = 2(2)^2 = 8 so those two expressions are not equal. when you add terms of the same variable, you just add their "coefficients," the number in front of the variable.

heisenberg
 3 years ago
Best ResponseYou've already chosen the best response.2no x is a variable, not a number. x can be *any* number

heisenberg
 3 years ago
Best ResponseYou've already chosen the best response.2no just add the numbers *in front* of the variable. x = 1x

heisenberg
 3 years ago
Best ResponseYou've already chosen the best response.2right! so now let's look at the original equation, what is \( a^2 + a^2 \)

heisenberg
 3 years ago
Best ResponseYou've already chosen the best response.2keep in mind that \(a^2 \) is the same thing as \(1a^2\)

heisenberg
 3 years ago
Best ResponseYou've already chosen the best response.2there are no x's in this equation. that was just as an aside example. the question here is to simplify \(a^2 + a^2\) you know that \( x + x = 2x\), so use that same *idea* and apply it to the other equation.

heisenberg
 3 years ago
Best ResponseYou've already chosen the best response.2you don't add the exponents, just the coefficients. \( x = 1x = x^1 = 1x^1 \) are all the same same

heisenberg
 3 years ago
Best ResponseYou've already chosen the best response.2very good! so let's look at our original equation: \(a^2 + a^2 = 36^2 \) = \(2a^2 = 36^2\)

heisenberg
 3 years ago
Best ResponseYou've already chosen the best response.2yes it is, that's how we eliminated the b^2 and replaced it with another a^2

heisenberg
 3 years ago
Best ResponseYou've already chosen the best response.2so now our equation is \(2a^2 = 36^2\) do you know how to solve algebra problems? that's all this is.

safia21
 3 years ago
Best ResponseYou've already chosen the best response.1so i multiply 36 times 36 and divide it by 2

heisenberg
 3 years ago
Best ResponseYou've already chosen the best response.2that would be represented like so: \(a^2 = \frac{36^2}{2} \) then you just take the square root of both sides to get 'a' = something

heisenberg
 3 years ago
Best ResponseYou've already chosen the best response.2not quite, remember, it's: 36 * 36 / 2

heisenberg
 3 years ago
Best ResponseYou've already chosen the best response.2first do 36 * 36, then divide that answer by 2

heisenberg
 3 years ago
Best ResponseYou've already chosen the best response.2very good! so we're left with: \( a^2 = 648\) just take the square root of both sides and you have your answer!

safia21
 3 years ago
Best ResponseYou've already chosen the best response.1but thats not one of the anwsers

heisenberg
 3 years ago
Best ResponseYou've already chosen the best response.2what are the answers?

safia21
 3 years ago
Best ResponseYou've already chosen the best response.1a) 18 b) 18√2 c) 36 d) 36√2

heisenberg
 3 years ago
Best ResponseYou've already chosen the best response.2well one of those answers roughly equals the number you got.

heisenberg
 3 years ago
Best ResponseYou've already chosen the best response.2that's right! congrats :)

heisenberg
 3 years ago
Best ResponseYou've already chosen the best response.2no problem :) i'm glad you wanted to learn rather than just want the answer. it'll always work out better that way. trust me ;)
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