In ΔABC, right-angled at B, AB = 7 cm and AC - BC = 1 cm. Find the value of sin C.

Question

Question

This question was previously asked in

SSC CGL 2022 Tier-I Official Paper (Held On : 02 Dec 2022 Shift 2)

Answer 1

Given:

In ΔABC, right-angled at B, AB = 7 cm and AC - BC = 1 cm.

Concept used:

1. In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides.

2. A² - B² = (A + B)(A - B)

3. sin θ = perpendicular ÷ Hypotenuse

Calculation:

F1 SSC Ishita 24.02.23 D8

AC - BC = 1 ....(1)

According to the concept,

AB² + BC² = AC²

⇒ 7² = AC² - BC² (∵ AB = 7)

⇒ (AC + BC)(AC - BC) = 49

⇒ (AC + BC) = 49 (∵ AC - BC = 1)

Solving, (1) and (2) we get, AC = 25 and BC = 24.

Now, sin C = \(\frac {7}{25}\)

∴ The value of sin C is \(\frac {7}{25}\).

Shortcut Trick

In the right-angled triangle one side AB = 7 and the other two sides difference is 1

Now, the only triplet 7,24,25 holds, so sin c = 7/25