I need help with this:
Given a right triangle with B=4 and
C=11 find A appoximated to three decimal places.
Use the Pythagorean theorem, r^2 = y^2 + x^2
r^2
= 4^2 + 11^2
= 16 + 121
= 137
= Square root of 137
= 11.705
This is how I would do it.
Pythagorean theorem: a2 + b2 = c2.
a^2 + 4^2 = 11^2
a^2 +16 = 105
subtract both sides by 16
a^2 - 16 = 105 - 16
a^2 = 105
a = sqrt 105
a = 10.247
To find side A of a right triangle with sides B and C, we can use the Pythagorean theorem, which states that the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, we have side B = 4 and side C = 11. Let's call the missing side A.
The Pythagorean theorem can be written as:
A^2 + B^2 = C^2
Substituting the given values:
A^2 + 4^2 = 11^2
Simplifying:
A^2 + 16 = 121
Subtracting 16 from both sides:
A^2 = 121 - 16
A^2 = 105
To find the value of A, we take the square root of both sides:
√(A^2) = √(105)
Simplifying:
A = √105
Now, to approximate A to three decimal places, you can use a calculator or a math software to find the square root of 105. The approximate value of A to three decimal places is 10.246.
So, side A is approximately 10.246 in this right triangle.