Advertisements
Advertisements
प्रश्न
Two poles of height 9m and 14m stand on a plane ground. If the distance between their 12m, find the distance between their tops.
Advertisements
उत्तर
Let AB and CD be the two poles of height 14m and 9m respectively.
It is given that BD = 12m
∴ CE = 12m
Now,
AE = AB - BE
= 14m - 9m = 5m
Using Pythagoras theorem in ΔACE,
AC2 = AE2 + CE2
= (5m)2 + (12m)2
= 25m2 = 144m2
= 169m2
= 13m2
⇒ AC = 13m
Thus, the distance between the tops of the poles is 13m.
APPEARS IN
संबंधित प्रश्न
In triangle ABC, ∠C=90°. Let BC= a, CA= b, AB= c and let 'p' be the length of the perpendicular from 'C' on AB, prove that:
1. cp = ab
2. `1/p^2=1/a^2+1/b^2`
In a right triangle ABC, right-angled at B, BC = 12 cm and AB = 5 cm. The radius of the circle inscribed in the triangle (in cm) is
(A) 4
(B) 3
(C) 2
(D) 1
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`
In a right triangle ABC right-angled at C, P and Q are the points on the sides CA and CB respectively, which divide these sides in the ratio 2 : 1. Prove that
`(i) 9 AQ^2 = 9 AC^2 + 4 BC^2`
`(ii) 9 BP^2 = 9 BC^2 + 4 AC^2`
`(iii) 9 (AQ^2 + BP^2 ) = 13 AB^2`
In a ∆ABC, AD ⊥ BC and AD2 = BC × CD. Prove ∆ABC is a right triangle
In Figure, ABD is a triangle right angled at A and AC ⊥ BD. Show that AB2 = BC × BD
Find the perimeter of the rectangle whose length is 40 cm and a diagonal is 41 cm.
The perimeter of a triangle with vertices (0, 4), (0, 0) and (3, 0) is
(A)\[7 + \sqrt{5}\]
(B) 5
(C) 10
(D) 12
Identify, with reason, if the following is a Pythagorean triplet.
(11, 60, 61)
In the given figure, ∠DFE = 90°, FG ⊥ ED, If GD = 8, FG = 12, find (1) EG (2) FD and (3) EF
In triangle ABC, AB = AC = x, BC = 10 cm and the area of the triangle is 60 cm2.
Find x.
In triangle ABC, AB = AC and BD is perpendicular to AC.
Prove that: BD2 − CD2 = 2CD × AD
In the given figure, angle BAC = 90°, AC = 400 m, and AB = 300 m. Find the length of BC.
Show that the triangle ABC is a right-angled triangle; if: AB = 9 cm, BC = 40 cm and AC = 41 cm
From the given figure, find the length of hypotenuse AC and the perimeter of ∆ABC.
If in a ΔPQR, PR2 = PQ2 + QR2, then the right angle of ∆PQR is at the vertex ________
Choose the correct alternative:
If length of sides of a triangle are a, b, c and a2 + b2 = c2, then which type of triangle it is?
In a right angled triangle, if length of hypotenuse is 25 cm and height is 7 cm, then what is the length of its base?
From given figure, In ∆ABC, If AC = 12 cm. then AB =?
Activity: From given figure, In ∆ABC, ∠ABC = 90°, ∠ACB = 30°
∴ ∠BAC = `square`
∴ ∆ABC is 30° – 60° – 90° triangle
∴ In ∆ABC by property of 30° – 60° – 90° triangle.
∴ AB = `1/2` AC and `square` = `sqrt(3)/2` AC
∴ `square` = `1/2 xx 12` and BC = `sqrt(3)/2 xx 12`
∴ `square` = 6 and BC = `6sqrt(3)`
The longest side of a right angled triangle is called its ______.
