Question

solve for c # 2
set up an equation that can be used to solve for the missing side length.
use c as your unknown.
then, solve the equation and if necessary, round your answer to the nearest tenth.
equation - here
submit
c =
submit

Explanation:

Step1: Apply Pythagorean theorem

Assume the two legs of the right - triangle are \(a\), \(b\) and the hypotenuse is \(c\). The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\). Here, if we assume the known side 15 is the hypotenuse and one of the legs is \(c\), and the other leg is \(x\) (not given), then \(c^{2}+x^{2}=15^{2}\), or if \(c\) is a leg and 15 is the hypotenuse, the equation is \(c^{2}+b^{2}=15^{2}\), so \(c^{2}=15^{2}-b^{2}\). Since only one side length 15 is given and we assume \(c\) is a leg, the equation is \(c^{2}=15^{2}-b^{2}\). If we assume the other leg is 0 (not a real - world triangle but for the sake of the formula with the given info), \(c^{2}=15^{2}-0^{2}\), but this is wrong. Let's assume \(c\) is a leg and the hypotenuse is 15. Let the other leg be \(a\). Then \(a^{2}+c^{2}=15^{2}\), and \(c^{2}=15^{2}-a^{2}\). Without knowing the other leg length, we can't get a numerical value. But if we assume this is a right - isosceles triangle (a special case) where the two legs are equal and \(c\) is a leg, and the hypotenuse \(h = 15\), then by \(a^{2}+a^{2}=h^{2}\), \(2c^{2}=15^{2}\), \(c^{2}=\frac{15^{2}}{2}\), \(c=\frac{15}{\sqrt{2}}\approx10.6\). The general equation for a right - triangle with hypotenuse 15 and \(c\) as a leg is \(c^{2}=15^{2}-a^{2}\), where \(a\) is the other leg. If we assume the triangle is a right - isosceles triangle:

Step2: Solve for \(c\)

Given \(2c^{2}=15^{2}\), \(c^{2}=\frac{225}{2}\), \(c=\sqrt{\frac{225}{2}}=\frac{15}{\sqrt{2}}\approx 10.6\)

Answer:

Equation: \(2c^{2}=15^{2}\) (assuming right - isosceles triangle)
\(c\approx10.6\)