Question

solve for x. round to the nearest tenth, if necessary.

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, \(a^{2}+b^{2}=c^{2}\). Here, \(a = 1.7\), \(b=x\), \(c = 1.9\). So, \(x^{2}+1.7^{2}=1.9^{2}\).

Step2: Simplify the equation

\(x^{2}=1.9^{2}-1.7^{2}\). Using the formula \(a^{2}-b^{2}=(a + b)(a - b)\), we have \(x^{2}=(1.9 + 1.7)(1.9 - 1.7)\). Then \(x^{2}=(3.6)\times(0.2)=0.72\).

Step3: Solve for \(x\)

Take the square root of both sides, \(x=\sqrt{0.72}\approx0.8\).

Answer:

\(0.8\)