Question

In ΔABC rightangled at B, BC = 6 cm and difference between length of other two sides is 2 cm. FInd the value of sinA + sinC + cosA + cosC.
1. 14/5
2. 16/10
3. 6/5
4. 7/5

Answer 1

Correct Answer - Option 1 : 14/5

Given-   

BC = 6 cm

Difference between length of other two sides = 2 cm

Concept Used-

Hypotenuse² = Perpendicular² + Base²

Calculation-

Let the length of other two sides be x and x + 2

According to Condition-

x² + 6² = (x + 2)²

⇒ x2 + 62 = x² + 4 + 4x

⇒ 4x = 32

⇒ x = 8

Hence, the three sides of the triangle are Perpendicular = 8, Base = 6 and Hypotenuse = 10

sinA + sinC + cosA + cosC

⇒ 8/10 + 6/10 + 6/10 + 8/10

⇒ 28/10

⇒ 14/5

∴ The value of sinA + sinC + cosA + cosC is 14/5