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How is Pythagoras and what did he do?
Pythagoras, a greek mathematician living about 2600 years ago, became immortalised simply by finding a method for calculating the length of the hypotenuse without having to draw it out
Why is Pythagoras' theorem useful?
well... one of its uses can be as follows: you see trigonometry deals with right angles right, so through the Pythagoras theorem you can find out the sides of the triangle, without which trig would be impossible!
How do you find the length of a hypotenuse without using the pythagorean theorem?
If you know one side (s) and the opposite angle (a) then the hypotenuse = s/sin a...
what- Triangle rigidity means that a triangle cannot be deformed without changing its?
side lengths
What triangle it has three sides and three angles?
Any and every triangle has three sides and three angles; that is the defintion. The type of triangle cannot be determined without more information.
What is the length of the hypotenuse of a triangle if the length of one side is 6 m and the other side 8 m?
To find the length of the hypotenuse on a triangle, you have to use the Pythogoras Theoram. using the equation a square + b square = c square. you cannot find it without using the pythagoras theoram
Can you tell if a triangle is congruent without using the hypotenuse theorem?
no not really
How is Pythagoras and what did he do?
Pythagoras, a greek mathematician living about 2600 years ago, became immortalised simply by finding a method for calculating the length of the hypotenuse without having to draw it out
A right triangle has a hypotenuse of 10 cm and one leg that measures What is the length of the other leg?
Without knowing the measurement of one of its legs it's impossible to work out using Pythagoras' theorem. So from an experienced guess the two legs could be 8 cm and 6 cm with an hypotenuse of 10 cm.
How do you work out the lengths of the sides of a triangle from the hypotenuse?
Without any further information, you can't.
What is the length of the hypotenuse of a right angle triangle when its height is 6 cm more than its base detailing your work?
Call the base "x", then the height would be "x+6". Now, use Pythagoras' formula to calculate the hypotenuse. Without more information, you can't know the specific length of the hypothenuse - only its relationship to the base (or to the height).
How do you find the height of a fight triangle when the hypotenuse is 9?
I guess you meant a right triangle with a hypotenuse of 9 units.Long answer:If the hypotenuse is used as the base of the triangle, the height will be any value greater than 0 units and less than or equal to 41/2 units.If one of the other two sides is used as the base, then the height will be any value greater than 0 units and less than 9 units such that height = √(81 - base2).Short answer:You can't without further information about one of the other two sides.Short answer expanded:Then you can use Pythagoras to find the third side.If one if the non-hypotenuse sides is the base, then the height is the other side.Otherwise with the hypotenuse as the base, the height is given by:height = product_of_the_other_two_sides ÷ hypotenuse
What is the answer.In this picture the dotted line represents a ladder. How high on the house does the ladder reach?
It appears to be a question that involves Pythagoras' theorem of a right angle triangle whereas the dotted line represents the hypotenuse and without any relevant information the height of the ladder from the ground can't be worked out.
Why do you think non-right triangles don't uphold the Pythagrean therom?
First of all, it is clear that a right angled triangle does conform to Pythagoras. So, take any rightangled triangle, and without changing the length of the small sides, slightly reduce the right-angle to something smaller. What was the hypotenuse is now smaller than it was, so its square is now smaller. But the sum of the squares of the other 2 sides hasn't changed. So the Pythagoras result does not work for this new situation.
Why is Pythagoras' theorem useful?
well... one of its uses can be as follows: you see trigonometry deals with right angles right, so through the Pythagoras theorem you can find out the sides of the triangle, without which trig would be impossible!
How do you find the area of an equilateral triangle without knowing the height?
You find the height by using Pythagoras' theorem and then 0.5*base*height = area.
What are the alternative ways of finding the length of the hypotenuse of a right angle triangle without using Pythagoras theorem?
The least accurate is to draw the triangle and then measuring it. Alternatively you can use trigonometric ratios: tan = opposite/adjacent sin = opposite/hypotenuse → hypotenuse = opposite/sin cos = adjacent/hypotenuse → hypotenuse = adjacent/cos Using the tangent ration one of the non-right angles of the triangle can be found. Then using either the sine or cosine ratio the hypotenuse can be found. eg if the two "legs" are 1 cm and √2 cm, then: The angle at the end of the √2 cm side is: arc tan(1/√2) = 30° Then the hypotenuse is: 1 cm / sin (arc tan(1/√2)) = 1 cm / ½ = 2 cm. or √2 / cos (arc tan(1/√2)) = √2 / (1/√2) = √2 × √2 = 2. eg if the two "legs" are 3 cm and 4 cm, then: The angle at the end of the 4 cm side is: arc tan ¾ ≈ 36.87° The the hypotenuse is: 3 / sin(arc tan ¾) = 3/0.6 = 5 or 4 / cos(arc tan ¾) = 3/0.8 = 5
