\(\triangle\)ABC, B पर एक समकोण त्रिभुज है और tan A = \(\frac{3}{4}\), तो sin A + sin B + sin C का मान क्या होगा?

This question was previously asked in
SSC CGL 2022 Tier-I Official Paper (Held On : 12 Dec 2022 Shift 2)
View all SSC CGL Papers >
  1. 2\(\frac{4}{5}\)
  2. \(2\frac{2}{5}\)
  3. \(3\frac{1}{5}\)
  4. \(1\frac{1}{5}\)

Answer (Detailed Solution Below)

Option 2 : \(2\frac{2}{5}\)
super-pass-live
Free
SSC CGL Tier 1 2025 Full Test - 01
3.3 Lakh Users
100 Questions 200 Marks 60 Mins

Detailed Solution

Download Solution PDF

दिया गया है:

ΔABC, B पर एक समकोण त्रिभुज है और tan A = \(\frac{3}{4}\)

प्रयुक्त अवधारणा:

1. tan θ = ऊँचाई ÷ आधार

2. sin θ =  ऊँचाई  ÷ कर्ण

3. पाइथागोरस प्रमेय के अनुसार "एक समकोण त्रिभुज में, कर्ण भुजा का वर्ग अन्य दो भुजाओं के वर्गों के योगफल के बराबर होता है"

गणना:

qImage64a6c3869d9e67a4b58380ba

tan A = \(\frac{3}{4}\)

⇒ \(\frac {BC}{AB}\)\(\frac{3}{4}\)

⇒ BC : AB = 3 : 4

माना BC और AB की माप क्रमशः 3k और 4k है।

अवधारणा के अनुसार,

AC2 = \(\sqrt { (3k)^2 + (4k)^2 }\) = 5k

अब, sin A + sin B + sin C

⇒ \(\frac {BC}{AC} + sin\ 90^\circ + \frac {AB}{AC}\)

⇒ \(\frac {BC + AB}{AC} + 1\)

⇒ \(\frac {3k + 4k}{5k} + 1\)

⇒ \(\frac {7}{5} + 1\)

⇒ \(\frac {12}{5}\) = \(2\frac{2}{5}\)

 sin A + sin B + sin C का मान \(2\frac{2}{5}\) है।

Latest SSC CGL Updates

Last updated on Jul 10, 2025

-> The SSC CGL Application Correction Window Link Live till 11th July. Get the corrections done in your SSC CGL Application Form using the Direct Link.

-> This year, the Staff Selection Commission (SSC) has announced approximately 14,582 vacancies for various Group B and C posts across government departments.

-> The SSC CGL Tier 1 exam is scheduled to take place from 13th to 30th August 2025.

->  Aspirants should visit ssc.gov.in 2025 regularly for updates and ensure timely submission of the CGL exam form.

-> Candidates can refer to the CGL syllabus for a better understanding of the exam structure and pattern.

-> The CGL Eligibility is a bachelor’s degree in any discipline.

-> Candidates selected through the SSC CGL exam will receive an attractive salary. Learn more about the SSC CGL Salary Structure.

-> Attempt SSC CGL Free English Mock Test and SSC CGL Current Affairs Mock Test.

Get Free Access Now
Hot Links: teen patti teen patti master apk teen patti master golden india teen patti - 3patti cards game teen patti live