Question

A , B and C form a triangle where ∠ B A C = 90 ∘ . A B = 0.5 mm and B C = 15.4 mm. Find the length of A C , giving your answer rounded to 1 decimal place.

Answer 1

15•4 mm

Explanation:

using sine rule

a÷ sinA=c ÷sinC

15•4÷sin90=0•5÷sinC

sinC =0•5 × sin90 ÷ 15•4

C =1•9°

A+B+C= 180

90+B+1•9=180

B= 88•2°

b÷sinB = a÷sinA

b÷sin88•2= 15•4÷sin90

b=sin88•2 ×15•4 ÷sin90

b =15•39

to 1 dp

b =15•4 mm