English
Maharashtra State BoardSSC (English Medium) 10th Standard

In right angle ΔABC, if ∠B = 90°, AB = 6, BC = 8, then find AC.

Advertisements
Advertisements

Question

In right angle ΔABC, if ∠B = 90°, AB = 6, BC = 8, then find AC.

Sum
Advertisements

Solution

In ΔABC, ∠B = 90°, AB = 6, BC = 8

By Pythagoras theorem,

AC2 = AB2 + BC2 

= 62 + 82 

= 36 + 64

AC= 100

∴ AC = 10 units

shaalaa.com
  Is there an error in this question or solution?
2018-2019 (March) Set 1

APPEARS IN

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

A man goes 10 m due east and then 24 m due north. Find the distance from the starting point


In the following figure, O is a point in the interior of a triangle ABC, OD ⊥ BC, OE ⊥ AC and OF ⊥ AB. Show that

(i) OA2 + OB2 + OC2 − OD2 − OE2 − OF2 = AF2 + BD2 + CE2

(ii) AF2 + BD2 + CE= AE2 + CD2 + BF2


Some question and their alternative answer are given. Select the correct alternative.

If a, b, and c are sides of a triangle and a+ b= c2, name the type of triangle.


Find the length of the hypotenuse of a right angled triangle if remaining sides are 9 cm and 12 cm.


In triangle ABC, AB = AC and BD is perpendicular to AC.

Prove that: BD2 − CD2 = 2CD × AD


In the following figure, OP, OQ, and OR are drawn perpendiculars to the sides BC, CA and AB respectively of triangle ABC.

Prove that: AR2 + BP2 + CQ2 = AQ2 + CP2 + BR2



In a quadrilateral ABCD, ∠B = 90° and ∠D = 90°.
Prove that: 2AC2 - AB2 = BC2 + CD2 + DA2


In the given figure, angle ACB = 90° = angle ACD. If AB = 10 m, BC = 6 cm and AD = 17 cm, find :
(i) AC
(ii) CD


Use the information given in the figure to find the length AD.


In the figure below, find the value of 'x'.


A ladder 15m long reaches a window which is 9m above the ground on one side of a street. Keeping its foot at the same point, the ladder is turned to other side of the street to reach a window 12m high. Find the width of the street.


Two trains leave a railway station at the same time. The first train travels due west and the second train due north. The first train travels at a speed of `(20 "km")/"hr"` and the second train travels at `(30 "km")/"hr"`. After 2 hours, what is the distance between them?


In triangle ABC, line I, is a perpendicular bisector of BC.
If BC = 12 cm, SM = 8 cm, find CS


If length of sides of a triangle are a, b, c and a2 + b2 = c2, then which type of triangle it is?


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)`


In ∆PQR, PD ⊥ QR such that D lies on QR. If PQ = a, PR = b, QD = c and DR = d, prove that (a + b)(a – b) = (c + d)(c – d).


Two rectangles are congruent, if they have same ______ and ______.


The foot of a ladder is 6 m away from its wall and its top reaches a window 8 m above the ground. Find the length of the ladder.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×