त्रिभुज ABC में, कोण B = 135° है, AB = 10√2 सेमी और BC = 14 सेमी है। AC की लंबाई क्या है?

This question was previously asked in
AAI Junior Assistant (Fire Service) Official Paper (Held On: 15 Nov 2022 Shift 1)
View all AAI Junior Assistant Papers >
  1. 20√2 सेमी
  2. 28 सेमी
  3. 26 सेमी
  4. 24√2 सेमी

Answer (Detailed Solution Below)

Option 3 : 26 सेमी
Free
ST 1: English
2.4 K Users
20 Questions 20 Marks 25 Mins

Detailed Solution

Download Solution PDF

दिया गया है:

त्रिभुज ABC में, कोण B = 135°, AB = 10√2 सेमी और BC = 14 सेमी।

प्रयुक्त सूत्र:

कोज्या नियम का उपयोग करने पर:

\(c^2 = a^2 + b^2 - 2ab \cos(C)\)

गणना:

5-5-2025 IMG-1083 Prakhar -5

माना, AB = c = 10√2 सेमी, BC = a = 14 सेमी, और AC = b है।

कोण B = 135°

कोज्या नियम का उपयोग करने पर:

\(b^2 = a^2 + c^2 - 2ac \cos(B)\)

\(b^2 = 14^2 + (10√2)^2 - 2 \times 14 \times 10√2 \times \cos(135°)\)

\(b^2 = 196 + 200 - 2 \times 14 \times 10√2 \times -\frac{1}{√2}\)

\(b^2 = 196 + 200 + 2 \times 14 \times 10\)

\(b^2 = 676\)

\(b = 26\) सेमी

∴ सही उत्तर विकल्प (3) है।

Latest AAI Junior Assistant Updates

Last updated on Apr 24, 2025

-> The AAI Junior Assistant Response Sheet 2025 has been out on the official portal for the written examination.

-> AAI has released 168 vacancies for Western Region. Candidates had applied online from 25th February to 24th March 2025.

-> A total number of 152 Vacancies have been announced for the post of Junior Assistant (Fire Service) for Northern Region.

-> Eligible candidates can apply from 4th February 2025 to 5th March 2025. 

-> Candidates who have completed 10th with Diploma or 12th Standard are eligible for this post.

-> The selection process includes a Computer Based Test, Document Verification, Medical Examination (Physical Measurement Test), Driving Test and a Physical Endurance Test.

-> Prepare for the exam with AAI Junior Assistant Previous year papers.

More Triangles Questions

More Geometry Questions

Get Free Access Now
Hot Links: teen patti wealth teen patti casino apk teen patti casino teen patti apk download teen patti online