Question

find st.
write your answer as an integer or as a decimal rounded to the nearest tenth.
st =

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle \( \triangle SUT\) with \( \angle S = 90^{\circ}\), by the Pythagorean theorem \(SU^{2}+ST^{2}=UT^{2}\). Let \(ST = x\), \(UT = 9.7\), and assume \(SU = 6.4\) (from the numbers on the right side of the screen which might be the lengths, though the problem statement is a bit unclear. If we assume these are the values for the sides of the right - triangle). Then \(x^{2}+6.4^{2}=9.7^{2}\).

Step2: Rearrange the formula

\(x^{2}=9.7^{2}-6.4^{2}\). Using the formula \(a^{2}-b^{2}=(a + b)(a - b)\), we have \(x^{2}=(9.7+6.4)(9.7 - 6.4)=(16.1)\times(3.3)=53.13\). Or directly calculate \(9.7^{2}=94.09\) and \(6.4^{2}=40.96\), then \(x^{2}=94.09-40.96 = 53.13\).

Step3: Solve for \(x\)

\(x=\sqrt{53.13}\approx7.3\)

Answer:

\(7.3\)