Question

How do I solve this problem?

Answer 1

C

Explanation:

Since AC is a tangent at C then ∠ACB = 90 and ΔABC is right

The area A of ΔABC = 0.5 × BC × AC ( A = 0.5 bh )

Calculate AC using Pythagoras' identity

The square on the hypotenuse AB is equal to the sum of the squares on the other 2 sides, that is

AC² + BC² = AB², substitute values

AC² + 4² = 8², that is

AC² + 16 = 64 ( subtract 16 from both sides )

AC² = 48 ( take the square root of both sides )

AC =
`√(48)` =
`√(16)` ×
`√(3)` = 4
`√(3)`, hence

Area of ΔABC = 0.5 × 4 × 4
`√(3)` = 8
`√(3)` → C