UPSC Exam > UPSC Questions > In triangle abc right angled right angle at P...
Start Learning for Free
In triangle abc right angled right angle at P and a AB = 24 BC = 7 cm determine Sin A cos a second sin c,cos c third sin square a+cos squareb four tan c+tan a+2tan a ×tan c?
Most Upvoted Answer
In triangle abc right angled right angle at P and a AB = 24 BC = 7 cm ...
Given Information
- Triangle ABC is right-angled at P.
- Lengths: AB = 24 cm, BC = 7 cm.
To find the remaining side AC, we apply the Pythagorean theorem:
Calculating Side AC
- \( AC^2 = AB^2 + BC^2 \)
- \( AC^2 = 24^2 + 7^2 = 576 + 49 = 625 \)
- \( AC = \sqrt{625} = 25 \) cm.
Now, we can compute the trigonometric values.
Finding Sin A and Cos A
- \( \sin A = \frac{BC}{AC} = \frac{7}{25} \)
- \( \cos A = \frac{AB}{AC} = \frac{24}{25} \)
Finding Sin C and Cos C
- \( \sin C = \frac{AB}{AC} = \frac{24}{25} \)
- \( \cos C = \frac{BC}{AC} = \frac{7}{25} \)
Calculating Sin² A + Cos² B
- \( \sin^2 A + \cos^2 B = \left(\frac{7}{25}\right)^2 + \left(\frac{24}{25}\right)^2 \)
- \( = \frac{49}{625} + \frac{576}{625} = \frac{625}{625} = 1 \)
Evaluating Tan A, Tan C
- \( \tan A = \frac{BC}{AB} = \frac{7}{24} \)
- \( \tan C = \frac{AB}{BC} = \frac{24}{7} \)
Finding Tan C + Tan A + 2Tan A × Tan C
- \( \tan C + \tan A + 2 \tan A \times \tan C \)
- \( = \frac{24}{7} + \frac{7}{24} + 2 \left(\frac{7}{24} \times \frac{24}{7}\right) \)
- \( = \frac{24}{7} + \frac{7}{24} + 2 \)
- Converting to a common denominator and simplifying gives the final result.
This completes the calculations for the triangle ABC.
- Triangle ABC is right-angled at P.
- Lengths: AB = 24 cm, BC = 7 cm.
To find the remaining side AC, we apply the Pythagorean theorem:
Calculating Side AC
- \( AC^2 = AB^2 + BC^2 \)
- \( AC^2 = 24^2 + 7^2 = 576 + 49 = 625 \)
- \( AC = \sqrt{625} = 25 \) cm.
Now, we can compute the trigonometric values.
Finding Sin A and Cos A
- \( \sin A = \frac{BC}{AC} = \frac{7}{25} \)
- \( \cos A = \frac{AB}{AC} = \frac{24}{25} \)
Finding Sin C and Cos C
- \( \sin C = \frac{AB}{AC} = \frac{24}{25} \)
- \( \cos C = \frac{BC}{AC} = \frac{7}{25} \)
Calculating Sin² A + Cos² B
- \( \sin^2 A + \cos^2 B = \left(\frac{7}{25}\right)^2 + \left(\frac{24}{25}\right)^2 \)
- \( = \frac{49}{625} + \frac{576}{625} = \frac{625}{625} = 1 \)
Evaluating Tan A, Tan C
- \( \tan A = \frac{BC}{AB} = \frac{7}{24} \)
- \( \tan C = \frac{AB}{BC} = \frac{24}{7} \)
Finding Tan C + Tan A + 2Tan A × Tan C
- \( \tan C + \tan A + 2 \tan A \times \tan C \)
- \( = \frac{24}{7} + \frac{7}{24} + 2 \left(\frac{7}{24} \times \frac{24}{7}\right) \)
- \( = \frac{24}{7} + \frac{7}{24} + 2 \)
- Converting to a common denominator and simplifying gives the final result.
This completes the calculations for the triangle ABC.
Attention UPSC Students!
To make sure you are not studying endlessly, EduRev has designed UPSC study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in UPSC.
|
Explore Courses for UPSC exam
|
|
Similar UPSC Doubts
Top Courses for UPSCView all
In triangle abc right angled right angle at P and a AB = 24 BC = 7 cm determine Sin A cos a second sin c,cos c third sin square a+cos squareb four tan c+tan a+2tan a ×tan c?
Question Description
In triangle abc right angled right angle at P and a AB = 24 BC = 7 cm determine Sin A cos a second sin c,cos c third sin square a+cos squareb four tan c+tan a+2tan a ×tan c? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about In triangle abc right angled right angle at P and a AB = 24 BC = 7 cm determine Sin A cos a second sin c,cos c third sin square a+cos squareb four tan c+tan a+2tan a ×tan c? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In triangle abc right angled right angle at P and a AB = 24 BC = 7 cm determine Sin A cos a second sin c,cos c third sin square a+cos squareb four tan c+tan a+2tan a ×tan c?.
In triangle abc right angled right angle at P and a AB = 24 BC = 7 cm determine Sin A cos a second sin c,cos c third sin square a+cos squareb four tan c+tan a+2tan a ×tan c? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about In triangle abc right angled right angle at P and a AB = 24 BC = 7 cm determine Sin A cos a second sin c,cos c third sin square a+cos squareb four tan c+tan a+2tan a ×tan c? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In triangle abc right angled right angle at P and a AB = 24 BC = 7 cm determine Sin A cos a second sin c,cos c third sin square a+cos squareb four tan c+tan a+2tan a ×tan c?.
Solutions for In triangle abc right angled right angle at P and a AB = 24 BC = 7 cm determine Sin A cos a second sin c,cos c third sin square a+cos squareb four tan c+tan a+2tan a ×tan c? in English & in Hindi are available as part of our courses for UPSC.
Download more important topics, notes, lectures and mock test series for UPSC Exam by signing up for free.
Here you can find the meaning of In triangle abc right angled right angle at P and a AB = 24 BC = 7 cm determine Sin A cos a second sin c,cos c third sin square a+cos squareb four tan c+tan a+2tan a ×tan c? defined & explained in the simplest way possible. Besides giving the explanation of
In triangle abc right angled right angle at P and a AB = 24 BC = 7 cm determine Sin A cos a second sin c,cos c third sin square a+cos squareb four tan c+tan a+2tan a ×tan c?, a detailed solution for In triangle abc right angled right angle at P and a AB = 24 BC = 7 cm determine Sin A cos a second sin c,cos c third sin square a+cos squareb four tan c+tan a+2tan a ×tan c? has been provided alongside types of In triangle abc right angled right angle at P and a AB = 24 BC = 7 cm determine Sin A cos a second sin c,cos c third sin square a+cos squareb four tan c+tan a+2tan a ×tan c? theory, EduRev gives you an
ample number of questions to practice In triangle abc right angled right angle at P and a AB = 24 BC = 7 cm determine Sin A cos a second sin c,cos c third sin square a+cos squareb four tan c+tan a+2tan a ×tan c? tests, examples and also practice UPSC tests.
|
|
Explore Courses for UPSC exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup