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Q10. In triangle ABC, AB=AC=7, measure angle A = 120. Let "K" be the area of the triangle. Find 4(K^2).?
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Q10. In triangle ABC, AB=AC=7, measure angle A = 120. Let "K" be the a...
Understanding Triangle ABC
In triangle ABC, we have the following specifications:
- AB = AC = 7 (isosceles triangle)
- Angle A = 120°
To find the area (K) of triangle ABC, we can use the formula for the area of a triangle given two sides and the included angle:
Area Formula
The area \( K \) can be calculated using the formula:
\[ K = \frac{1}{2} \times AB \times AC \times \sin(A) \]
Substituting the known values:
\[ K = \frac{1}{2} \times 7 \times 7 \times \sin(120°) \]
Calculating \( \sin(120°) \)
Since \( \sin(120°) = \sin(180° - 60°) = \sin(60°) = \frac{\sqrt{3}}{2} \):
- Substitute \( \sin(120°) \) into the area formula:
\[ K = \frac{1}{2} \times 7 \times 7 \times \frac{\sqrt{3}}{2} \]
Final Calculation
Calculating \( K \):
\[ K = \frac{49\sqrt{3}}{4} \]
Finding \( 4(K^2) \)
Next, we need to find \( 4(K^2) \):
1. Calculate \( K^2 \):
\[ K^2 = \left(\frac{49\sqrt{3}}{4}\right)^2 = \frac{2401 \times 3}{16} = \frac{7203}{16} \]
2. Now, multiply by 4:
\[ 4(K^2) = 4 \times \frac{7203}{16} = \frac{7203}{4} = 1800.75 \]
Conclusion
Thus, the value of \( 4(K^2) \) is \( 1800.75 \).
In triangle ABC, we have the following specifications:
- AB = AC = 7 (isosceles triangle)
- Angle A = 120°
To find the area (K) of triangle ABC, we can use the formula for the area of a triangle given two sides and the included angle:
Area Formula
The area \( K \) can be calculated using the formula:
\[ K = \frac{1}{2} \times AB \times AC \times \sin(A) \]
Substituting the known values:
\[ K = \frac{1}{2} \times 7 \times 7 \times \sin(120°) \]
Calculating \( \sin(120°) \)
Since \( \sin(120°) = \sin(180° - 60°) = \sin(60°) = \frac{\sqrt{3}}{2} \):
- Substitute \( \sin(120°) \) into the area formula:
\[ K = \frac{1}{2} \times 7 \times 7 \times \frac{\sqrt{3}}{2} \]
Final Calculation
Calculating \( K \):
\[ K = \frac{49\sqrt{3}}{4} \]
Finding \( 4(K^2) \)
Next, we need to find \( 4(K^2) \):
1. Calculate \( K^2 \):
\[ K^2 = \left(\frac{49\sqrt{3}}{4}\right)^2 = \frac{2401 \times 3}{16} = \frac{7203}{16} \]
2. Now, multiply by 4:
\[ 4(K^2) = 4 \times \frac{7203}{16} = \frac{7203}{4} = 1800.75 \]
Conclusion
Thus, the value of \( 4(K^2) \) is \( 1800.75 \).
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Q10. In triangle ABC, AB=AC=7, measure angle A = 120. Let "K" be the area of the triangle. Find 4(K^2).?
Question Description
Q10. In triangle ABC, AB=AC=7, measure angle A = 120. Let "K" be the area of the triangle. Find 4(K^2).? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Q10. In triangle ABC, AB=AC=7, measure angle A = 120. Let "K" be the area of the triangle. Find 4(K^2).? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Q10. In triangle ABC, AB=AC=7, measure angle A = 120. Let "K" be the area of the triangle. Find 4(K^2).?.
Q10. In triangle ABC, AB=AC=7, measure angle A = 120. Let "K" be the area of the triangle. Find 4(K^2).? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Q10. In triangle ABC, AB=AC=7, measure angle A = 120. Let "K" be the area of the triangle. Find 4(K^2).? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Q10. In triangle ABC, AB=AC=7, measure angle A = 120. Let "K" be the area of the triangle. Find 4(K^2).?.
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