Chapter 10.8, Problem 11WE

To determine

To construct: isosceles $\Delta ABC$ so that $m\angle C=90,m\angle A=n$ , and the altitude to $\overline{AB}$ has length $s$ .

Explanation of Solution

Given Information:

Use figure,

  

Calculation:

Draw a line $m$ .

Draw $m\angle A=n$ at point $A$ on line $m$ .

Construct a perpendicular on line $m$ at $X$ .

Cut an arc of length $s$ on this perpendicular line.

Construct a perpendicular at $C$ . Line $l$ is parallel to line $m$ . Join point $A$ to point $C$ . Construct a perpendicular on line $\overline{AC}$ at point $C$ .

Join this perpendicular line extend it till this line meet to line $m$ . Intersecting point is the point $B$ .

Hence, $\Delta ABC$ is the required triangle.