How to use Pythagoras Theorem?
Pythagoras Theorem is defined as the way in which you can find the missing length of a right angled triangle.
The triangle has three sides, the hypotenuse (which is always the longest),
Opposite (which doesn't touch the hypotenuse) and the adjacent (which is between the opposite and the hypotenuse).
Pythagoras is in the form of;
a² + b² = c²
First triangle give numbers 7 and 10.
the second triangle gives 3 and a variable x. But the 2 triangles are combined together
So, to use Pythagoras Theorem in this scenario, you would first identify which sides of the triangle are the a, b, and c in the equation.
In the first triangle, let's say side a = 7 and side b = 10. To find the length of the hypotenuse (side c), you would plug these values into the Pythagoras equation: 7² + 10² = c².
Solving this equation, you would get 49 + 100 = c², which simplifies to 149 = c². Taking the square root of both sides gives you c ≈ 12.21. So, the length of the hypotenuse in the first triangle is approximately 12.21.
In the second triangle, let's say side a = 3 and the length of the hypotenuse (side c) is the variable x. Since the two triangles are combined, you would use the same Pythagoras equation: 3² + x² = 12.21².
Solving this equation, you would get 9 + x² = 149. Simplifying, you get x² = 140. Taking the square root of both sides, you get x ≈ 11.83. So, the missing length of the second triangle is approximately 11.83 using Pythagoras Theorem.
yeah but the 2 triangles are stuck together
I apologize for the confusion. If the two triangles are stuck together, you would need to consider the combined shape as a single triangle for the purposes of applying Pythagoras Theorem.
In this case, you can consider the combined shape as one large right-angled triangle, where the sides of the smaller triangles are the a and b in the Pythagoras equation, and the hypotenuse of the large triangle is the c in the equation.
So, for the combined shape with sides 3 and 7, and the unknown hypotenuse, you would use the Pythagoras formula: 3² + 7² = c².
This simplifies to 9 + 49 = c², or 58 = c². Taking the square root of both sides gives c ≈ 7.62. Therefore, the missing length of the combined triangle is approximately 7.62.
I hope this helps clarify how to use Pythagoras Theorem when dealing with triangles that are stuck together or combined. Let me know if you have any other questions.
How to use Pythagoras Theorem?
Pythagoras Theorem is defined as the way in which you can find the missing length of a right angled triangle.
The triangle has three sides, the hypotenuse (which is always the longest),
Opposite (which doesn't touch the hypotenuse) and the adjacent (which is between the opposite and the hypotenuse).
Pythagoras is in the form of;
a² + b² = c²
First triangle give numbers 7 and 10.
the second triangle gives 3 and a variable x. But the 2 triangles are combined together.Solve for x. Leave your answer in simplest radical form.
To solve for the variable x in the combined triangle with sides measuring 3 and x, and given that the hypotenuse is 10 (from the first triangle), you can use Pythagoras Theorem.
The Pythagorean Theorem states that for a right triangle with sides a, b, and hypotenuse c, a² + b² = c².
In this case, the values we have are 3 (side) and x (side), and the hypotenuse (c) is 10.
So, you would set up the equation as:
3² + x² = 10²
9 + x² = 100
x² = 100 - 9
x² = 91
Taking the square root of both sides to isolate x, we have:
x = √91
Therefore, the missing length x in the combined triangle is √91, and this is the simplest radical form of the answer.
First triangle give numbers 4,6,1 and Solve for xx to the nearest tenth.
It seems like there is some confusion in the information provided. In the context of Pythagoras Theorem, the sides of a right-angled triangle are typically denoted as a, b, and c, with c being the hypotenuse (the longest side).
If the first triangle has sides measuring 4, 6, and 10 (assuming the 10 is meant to be the hypotenuse), we can use Pythagoras Theorem to solve for the missing side, x.
Using the formula a² + b² = c²:
4² + 6² = x²
16 + 36 = x²
52 = x²
To find the value of x, we take the square root of 52:
x = √52 ≈ 7.2
Therefore, the missing length in the triangle is approximately 7.2.