14) Thevaluesof x and y for the right triangle are.15) The values of x, y, and z for theright triangleare,, and.Given are right triangles.14) Here, the length of thehypotenuseis 6.It is required to find thelengthof the two legs.Theangleopposite the hypotenuse is 90°.Another angle = 45°.So, by theangle sumproperty of triangles, the third angle is also 45°.So, the sides opposite these angles will be equal.So, x = y.By thePythagorean theorem:Since x = y,Squareboth sides.Divide both sides by 2.Take thesquare rooton both sides.15) There are two right triangles given.Consider the right triangle on the left.Hypotenuse =.Let m denote the unnamed side of thistrianglewhich is common to both right triangles.Since one of the angles is 45°, the other is also 45°.So, m = z.So, using the Pythagorean theorem:Divideboth sides by 2.Take the square root on both sides.From the other triangle, using the angle sum property, the third angle = 30°.The side opposite 60° = z = 24.Theratioof the sides for the 30°-60°-90° triangle is 1 : √3 : 2.Here,.So,.And,.So,.Hence the values of x and y arefor the first one, and the values of,, and.Learn more aboutPythagorean Theoremhere :brainly.com/question/14930619#SPJ6...

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