Question

Construct an isosceles triangle using the given data: Altitude XT = 6.8cm and vertex ∠X = 30°

Answer 1

Altitude XT = 6.8cm and vertex ∠X = 30°

Steps of construction:
1. Draw a line SU of any length.
2. Take a point T on SU.
3. Through the point T on SU draw NT perpendicular to SU.
4. With T as centre and radius 6.8cm, draw an arc to cut NT at X.
5. Construct ∠TXY = ∠TXZ = `(1)/(2) xx 30°` = 15°.
(a) With X as centre, draw an arc cutting XT at L..
(b) With L as centre and same radius, cut the arc at P and Q.
(c) Join PX and QX.
(d) Bisect ∠PXT and ∠QXT. Let XA and XB be the bisectors.
(e) Again bisect ∠AXT and ∠BXT. Let XR and XV be the bisectors. XR and XV make an angle of 15° with XT.
(f) Mark the points as Y and Z where XR and XV meet SU.
Thus, XYZ is the required triangle.