Advertisements
Advertisements
प्रश्न
In the given figure, AD = 13 cm, BC = 12 cm, AB = 3 cm and angle ACD = angle ABC = 90°. Find the length of DC.
Advertisements
उत्तर
Given :
∆ ACD = ∠ABC = 90°
and AD = 13 cm, BC = 12 cm, AB = 3 cm
To find : Length of DC.
(i) In right angled ∆ ABC
AB = 3 cm, BC = 12 cm
According to Pythagoras Theorem,
(AC)2 = (AB)2 + (BC)2
(AC)2 = (3)2 + (12)2
(AC) =`sqrt(9+144)=sqrt153` cm
(ii) In right angled ∆ ACD
AD = 13 cm, AC =`sqrt153`
According to Pythagoras Theorem,
DC2 = AB2 − AC2
DC2= 169 − 153
DC = `sqrt16` = 4 cm
∴ Length of DC is 4 cm
APPEARS IN
संबंधित प्रश्न
In an equilateral triangle, prove that three times the square of one side is equal to four times the square of one of its altitudes.
In the given figure, ABC is a triangle in which ∠ABC < 90° and AD ⊥ BC. Prove that AC2 = AB2 + BC2 − 2BC.BD.
Which of the following can be the sides of a right triangle?
1.5 cm, 2 cm, 2.5 cm
In the case of right-angled triangles, identify the right angles.
In right angle ΔABC, if ∠B = 90°, AB = 6, BC = 8, then find AC.
Find the length of diagonal of the square whose side is 8 cm.
Find the length of the perpendicular of a triangle whose base is 5cm and the hypotenuse is 13cm. Also, find its area.
The foot of a ladder is 6m away from a wall and its top reaches a window 8m above the ground. If the ladder is shifted in such a way that its foot is 8m away from the wall to what height does its tip reach?
Find the unknown side in the following triangles
A flag pole 18 m high casts a shadow 9.6 m long. Find the distance of the top of the pole from the far end of the shadow.
Two angles are said to be ______, if they have equal measures.
