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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?
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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.
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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?
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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?.
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