Question

ABC and ADC are triangles.

118°

105

11 m

The area of triangle ADC is 56 m²

Work out the length of AB.

Give your answer correct to 1 decimal place.

Answer 1

Explanation:

here ABC and ADC are triangles

using ΔADC

1/2 × x ×11 ×sin 105° = 56

x= 56×2/ 11 sin105° =10.5409

cosine rule to find AC

(AC)²= 11²+ (10.5409)²-2×11×10.5409×cos 105°

(AC)²= 292.13317

AC= 17.09190364

On ΔABC use the sine rule

AB/sin 48°= 17.09190364 /sin 118°

AB = 17.09190364 ×sin 48°/ sin 118°

= 14.38563

= 14.4 m