Question

PLEASE HELP! 15 POINTS!

ABC and is a straight line

Work out the length of AC
Give your answer to 1 decimal place

Answer 1

AC ≈ 19.2 cm

Explanation:

Using Pythagoras' identity in Δ BCD to find BC

BC² + BD² = DC² , that is

BC² + 12.6² = 19.3²

BC² + 158.76 = 372.49 ( subtract 158.76 from both sides )

BC² = 213.73 ( take the square root of both sides )

BC =
`√(213.73)` ≈ 14.62

Using the tangent ratio in Δ ABD to find AB

tan20° =
`(opposite)/(adjacent)` =
`(AB)/(BD)` =
`(AB)/(12.6)` ( multiply both sides by 12.6 )

12.6 × tan20° = AB , then

AB ≈ 4.59

Then

AC = AB + BC = 14.62 + 4.59 ≈ 19.2 cm ( to 1 dec. place )

Answer 2

19.2

Explanation:

I hope it helps you.....