Triangle equation.?

Question

A 30 degrees-60degrees-90degrees triangle that has one leg of lenght 1 and the hypotenuse of lenth 2 units. Call this triangle T1. (note that the answer that you get from the calculator on this problem is not the exact answer but is an approximation of the answer. Do not use your calculator answer but find the answer algebraically!)

What is the name of the process that allows you to calculate the lenght of the other leg of this triangle?

What is the formula?

Calculate the exact calue length of the second leg (x)

Note-1 is on the left side of the triangle 90 degrees. 2 is on the right side. (x) is at the bottom.

Answer 1

pythagereon theorem is what it's called.
equation:
side1 squared + side2 squared = hypoteneus squared.
plug in the numbers
1squared + x squared = 2 squared
1+xsquared=4
x=square root of 3.

Answer 2

"base is 8 cm longer than height" ==> b = h + 8 Area of a triangle = 1/2 b * h = 1/2 (h + 8)h 1/2 (h + 8)h comes from replacing b with h + 8 from first step Area = 1/2 (h^2 + 8h) = 24 (distribute the h) h^2 + 8h = 48 (multiply both sides by 2) h^2 + 8h - 48 = 0 (subtract 48 from both sides) (h + 12)(h - 4) = 0 (factor) This means either factor = 0 If h + 12 = 0, h = -12 h = -12 (not valid for length) or h = 4 If h - 4 = 0, then h = 4 and b = 4 + 8 = 12 = base check 1/2 (4 * 12)= 24 yep -------------------------- x² - 6x - 4 = 0 There's a technique called completing the square for solving problems like this: x^2 - 6x + ______ = 4 + _______ (add 4 to both sides) remember the general form of (x + a)^2 = x^2 + 2ax + a^2 what we have is -6x = 2ax, or a = -3 and a^2 = 9 so if we add 9 to both sides, that will make the left side a perfect square (x - 3)^2 x^2 - 6x + 9 = 4 + 9 = 13 (add it to both sides to keep the equation balanced) (x - 3)^2 = 13 take the square root of both sides, but remember that it can be + or -... x - 3 = +/- sqrt(13) now, adding 3 to both sides gives: x = 3 +/- sqrt(13) which means there are 2 solutions hidden in there: x = 3 + sqrt(13) x = 3 - sqrt(13) ------------------------- sbhmechanical-- I agree with you; but what happens sometimes (with at least the first few answers) is that people are answering at the same time. Why people add the same response after 5 or 10 minutes (or 2 or 3 hours) is a mystery!

Answer 3

A^2 + B^2 = C^2 ->pythagoras equation
A and B are edges of triangle, and C is the hypotenuse

in your case A = 1 and C = 2, solve for B
A^2 = 1^2 = 1
C^2 = 2^2 = 4
1 + B^2 = 4, B^2 = 3, B = sqrt(3)

Answer 4

You use the Theorem of Pythagoras, which states that in any right angled triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides.

In T1, the hypotenuse is 2, and the length of one of the other two sides is 1, so:

2^2 = 1^2 + x^2, so

4 = 1 + x^2, so

3 = x^2, so

x = sqrt3.

Hope this helps, Twiggy.

Answer 5

The easiest way is by using the pythagorean theorum, which would be:
a^2 + b^2 = c^2
a^2 + 1^2 = 2^2
a^2 + 1 = 4
a^2 = 3
a = sqrt(3)

You could also use sin or cos, or even sec or csc.

a = 2(sin 60*)
a = 2(cos 30*)

But pythagoras gave a very simple way to solve this; why not use it?

Answer 6

A^2 + B^2 = C^2

Since C = 2 and A = 1 B = 3, because 2^2 - 1^2 = 4 - 1 = 3.

Answer 7

i think you are confused . everything is correct
this is a right triangle
here is my solution:

sine30=1/2=0.5....ok
cosine 30 =√3/2=0.866 ok
tan 30=1/√3= ok

if you use phytagorean theorem same
2²=1²+(√3)²
4=4??? where is the problem???

answer # 1 use phytagorean theorem
answer # 2 h²=a²+o²

by the way this is a special triangle check your calculator it might be in wrong setting either it is in radian setting or grad. setting

Answer 8

I think the name of the process is the Pythagorean Theorem.

Try applying that to this triangle to get the length of the side.

Answer 9

c^2 = a^2 + b^2 (Pythagorean theorem)

2^2 = 1^2 + b^2
b = sqrt(3)

Answer 10

30,60,90 IS EASY. IF T=HYPOT. T/2 IS THE SHORT SIDE, AND T/2 X THE SQUARE ROOT OF 3 IS THE OTHER SIDE. OR SHORT SIDE TIME 1.732