Q16 of 27 Page 289

In the triangle ABC the perpendicular AD from the point A on the side BC meets the side BC at the point D. If BD = 8cm, DC = 2cm. and AD = 4cm., then let us write the measure of ∠BAC.


Given: BD = 8 cm


DC = 2 cm


AD = 4 cm


By applying Pythagoras theorem to ΔACD we get,


AC2 = AD2 + CD2


AC2 = 42 + 22


AC2 = 16 + 4


AC2 = 20 ……………………… (1)


By applying Pythagoras theorem to ΔABD we get,


AB2 = AD2 + BD2


AB2 = 42 + 82


AB2 = 16 + 64


AB2 = 80 ……………………… (2)


Now,


BC = BD + DC


BC = 8 + 2


BC = 10


BC2 = 102 = 100 ……………… (3)


By adding eqns. (1) and (2) and equating with (3) we get,


BC2 = AB2 + AC2


⇒ h2 = p2 + b2


OR,


∠BAC is a right angle.


More from this chapter

All 27 →
16

In ΔABC, if AB = (2a-1)cm. AC = 2 √2acm. And BC = (2a + 1)cm., then let us write the value of ∠BAC.

 16

In the adjoining figure, the point O is situated within the triangle PQR in such a way that ∠POQ = 90°, OP = 6cm. and OQ = 8cm. If PR = 24cm. and ∠QPR = 90°, then let us write the length of QR.

 16

The point O is situated within the rectangular figure ABCD in such a way that OB = 6 cm., OD = 8cm. and OA = 5cm. Let us determine the length of OC.

 16

In a right angled triangle ∠ABC, ABC = 90°, AB = 3cm., BC = 4cm. and the perpendicular BD on the side AC from the point B which meets the side AC at the point D. Let us determine the length of BD.