Advertisements
Advertisements
Question
Two trees 7 m and 4 m high stand upright on a ground. If their bases (roots) are 4 m apart, then the distance between their tops is ______.
Options
3 m
5 m
4 m
11 m
Advertisements
Solution
Two trees 7 m and 4 m high stand upright on a ground. If their bases (roots) are 4 m apart, then the distance between their tops is 5 m.
Explanation:
Let BE be the smaller tree and AD be the bigger tree.
Now, we have to find AB (i.e. the distance between their tops).
By observing,
ED = BC = 4 m and BE = CD = 4 m
In ΔABC, BC = 4 m
And AC = AD – CD = (7 – 4) m = 3 m
In right angled ΔABC,
AB2 = AC2 + BC2 ...[By Pythagoras theorem]
= 42 + 32
= 16 + 9
⇒ AB2 = 25
⇒ AB = `sqrt(25)`
⇒ AB = 5 m
Therefore, the distance between their tops is 5 m.
APPEARS IN
RELATED QUESTIONS
From a point O in the interior of a ∆ABC, perpendicular OD, OE and OF are drawn to the sides BC, CA and AB respectively. Prove
that :
`(i) AF^2 + BD^2 + CE^2 = OA^2 + OB^2 + OC^2 – OD^2 – OE^2 – OF^2`
`(ii) AF^2 + BD^2 + CE^2 = AE^2 + CD^2 + BF^2`
D and E are points on the sides CA and CB respectively of a triangle ABC right angled at C. Prove that AE2 + BD2 = AB2 + DE2
In the given figure, AD is a median of a triangle ABC and AM ⊥ BC. Prove that:
`"AC"^2 = "AD"^2 + "BC"."DM" + (("BC")/2)^2`
Which of the following can be the sides of a right triangle?
2 cm, 2 cm, 5 cm
In the case of right-angled triangles, identify the right angles.
A man goes 40 m due north and then 50 m due west. Find his distance from the starting point.
In the given figure, AB//CD, AB = 7 cm, BD = 25 cm and CD = 17 cm;
find the length of side BC.
Diagonals of rhombus ABCD intersect each other at point O.
Prove that: OA2 + OC2 = 2AD2 - `"BD"^2/2`
A boy first goes 5 m due north and then 12 m due east. Find the distance between the initial and the final position of the boy.
In a right-angled triangle ABC,ABC = 90°, AC = 10 cm, BC = 6 cm and BC produced to D such CD = 9 cm. Find the length of AD.
To get from point A to point B you must avoid walking through a pond. You must walk 34 m south and 41 m east. To the nearest meter, how many meters would be saved if it were possible to make a way through the pond?
