In ΔABC, AB = 7 cm, BC = 24 cm and AC = 25 cm. Find the value of tanC + sinC + 2cotA.
Show answer & explanation
Correct answer: C
Explanation
Has been given :
AB = 7 cm
BC = 24 cm
AC = 25 cm
According to the formula:
in a right triangle
sinθ = opposite side/hypotenuse
tanθ = opposite side / adjacent side
cotθ = adjacent side / opposite side
7² + 24² = 49 + 576 = 625 = 25²
Hence ∠B = 90°
tanC = AB / BC = 7 / 24
sinC = AB / AC = 7 / 25
cotA = AB / BC = 7 / 24
tanC + sinC + 2cotA= 7/24 + 7/25 + 2(7/24)
= 7/24 + 7/25 + 14/24
= 21/24 + 7/25
= 7/8 + 7/25
= (175 + 56) / 200 = 231 / 200 = 1.155