In ABC , B = 90^ , BC = 7 cm . If AC - AB = 1 cm , then the value of A (denoted here as θ for the targeted angle) is: - Quantitative Aptitude MCQ Competitive Examination 2026 | ExamTest.live

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In △ A BC, ∠ B = 9 0^{\circ}, BC = 7 cm . If A C - A B = 1 cm, then the value of sin A (denoted here as sin θ for the targeted angle) is:

Solution & Step-by-step Explanation

In right-angled △ A BC at B, by Pythagoras' theorem: A C^{2} = A B^{2} + B C^{2} Given BC = 7 cm and A C - A B = 1 ⟹ A C = A B + 1 . (A B + 1)^{2} = A B^{2} + 7^{2} A B^{2} + 2 A B + 1 = A B^{2} + 49 2 A B = 48 ⟹ A B = 24 cm Then, A C = 24 + 1 = 25 cm . For angle A (θ): sin A = \frac{Opposite side}{Hypotenuse} = \frac{BC}{A C} = \frac{7}{25}

Try it yourself before checking the explanation above.

In △ A BC, ∠ B = 9 0^{\circ}, BC = 7 cm . If A C - A B = 1 cm, then the value of sin A (denoted here as sin θ for the targeted angle) is:

7/24

7/25

24/25

25/24

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