Question

find z.
triangle with 7 mm side, two 45° angles, right angle
write your answer in simplest radical form.
blank millimeters
√ button

Explanation:

Step1: Identify the triangle type

This is a \(45^{\circ}-45^{\circ}-90^{\circ}\) right - triangle. In a \(45^{\circ}-45^{\circ}-90^{\circ}\) triangle, the sides are in the ratio \(1:1:\sqrt{2}\). Let the legs be of length \(a\) (one leg is \(7\) mm) and the hypotenuse be \(z\). The formula for the hypotenuse \(z\) of a \(45^{\circ}-45^{\circ}-90^{\circ}\) triangle is \(z = a\sqrt{2}\), where \(a\) is the length of a leg.

Step2: Substitute the value of \(a\)

Since \(a = 7\) mm, substituting into the formula \(z=a\sqrt{2}\), we get \(z = 7\sqrt{2}\) mm.

Answer:

\(7\sqrt{2}\)