Question

Calculate size of angle x. I worked out CA=14cm

Answer 1

x = 41.2 (to 3 s.f)

Explanation:

CD = 22-6= 16

AC = 14

tan (x) = Opposite/ Adjacent

tan (x) = 14/16

tan^-1(14/16) = 41.18592517

x = 41.18592517

x = 41.2 (to 3 s.f)

Answer 2

∠x = 13.43°

Explanation:

area ΔABC = 1/2 ( BD x AC) = 1/2 (22 x AC) = 42

22 x AC = 84 AC = 84/22 = 42/11 = 3.82

CD = BD - BC = 22 - 6 = 16

AD² = AC² + CD² = (3.82)² + 16² = 270.59

AD = 16.45

sin ∠x = AC / AD = 3.82 / 16.45 = 0.2322

∠x = 13.43°