Question

question 4 (1 point) determine the length of side \\( \overline{st} \\). round to the nearest tenth, if necessary.
blank 1:
st = ____

Explanation:

Step1: Identify triangle type

It's a right - triangle with hypotenuse \( RT = 14.7 \) and one leg \( RS=8.2 \), and we need to find the other leg \( ST \). Use the Pythagorean theorem \( a^{2}+b^{2}=c^{2} \), where \( c \) is the hypotenuse, and \( a,b \) are the legs. Let \( ST = x \), \( RS = 8.2 \), \( RT=14.7 \). So \( x^{2}+8.2^{2}=14.7^{2} \).

Step2: Solve for \( x \)

First, calculate \( 8.2^{2}=67.24 \) and \( 14.7^{2}=216.09 \). Then \( x^{2}=216.09 - 67.24=148.85 \). Take the square root of \( 148.85 \): \( x=\sqrt{148.85}\approx12.2 \).

Answer:

\( 12.2 \)