Given two similar triangles, find a' to two significant digits if a = 8.6 * 10^4, b = 1.5 * 10^5, and b' = 1.3 * 10^4.
a' ÷ a = b' ÷ b
so
a' = b' × a / b
thanks!
You're welcome!
To find the length of side a' in the second triangle, we can set up a proportion using the corresponding sides of the two triangles.
The proportion can be written as:
a / b = a' / b'
Plugging in the given values:
8.6 * 10^4 / 1.5 * 10^5 = a' / 1.3 * 10^4
To simplify, we can divide both sides of the equation by 1.3 * 10^4:
(8.6 * 10^4 / 1.5 * 10^5) * (1 / 1.3 * 10^4) = a'
Simplifying further:
(8.6 / 1.5) * (10^4 / 10^5) * (1 / 1.3) = a'
Calculating this expression:
5.733333333333333 * 10^(4-5) * 1/1.3 = a'
Now we can multiply the numbers and simplify the scientific notation:
5.733333333333333 * 10^(-1) * 1/1.3 ~= 0.441743252 * 10^(-1)
To two significant digits, this is approximately:
0.44 * 10^(-1)
Converting back to scientific notation:
0.44 * 10^(-1) = 4.4 * 10^(-2)
Therefore, a' is approximately 4.4 * 10^(-2) to two significant digits.