Question

A student is writing a formula for the area of triangle xyz in terms of only the sides and angles. her first step is shown. a right triangle xyz with z as the length from yx and y as the base of xz and x as the height of yz. a straight line h from y intercepts the base of xz at a right angle. what step should the student take next? define h as define z in terms of h define h as define y in terms of h

Answer 1

The next step in writing the formula for the area of triangle XYZ is to define z (the hypotenuse) as z = √h² + y² using the Pythagorean theorem.

Step-by-step explanation:

The student is working on a formula for the area of a right triangle using the lengths of the sides and angles. Considering that the triangle XYZ is a right triangle with angle Z being the right angle, side YZ as height (h), and side XZ as base (y), the next step would be to employ the Pythagorean theorem, which relates the legs of a right triangle with the hypotenuse. The formula for the area can be expressed as 1/2 × base × height, and using the Pythagorean theorem, the relationship is c = √(a² + b²) for a right triangle with legs a and b and hypotenuse c. Since h is the height and y is the base, the next step for the student should be to define z (the hypotenuse) as z = √h² + y². This allows the student to express the area of the triangle in terms of h and y.