Question

In a right angled triangle ABC, right angle at A, if AB = 8cm and AC = 6cm, find the value of sinC and cosB.

Answer 1

sinC =
`(4)/(5)` , cosB =
`(4)/(5)`

Explanation:

To obtain the ratios we require to find the hypotenuse BC

Using Pythagoras' identity

BC² = AB² + AC² = 8² + 6² = 64 + 36 = 100 ( take square root of both sides )

BC =
`√(100)` = 10

Then

sinC =
`(opposite)/(hypotenuse)` =
`(AB)/(BC)` =
`(8)/(10)` =
`(4)/(5)`

cosB =
`(adjacent)/(hypotenuse)` =
`(AB)/(BC)`=
`(8)/(10)` =
`(4)/(5)`