Question

ABC is a right angled triangle
AC=16cm
Angle C=90
Size of angle B:size of angle A=3:2
Work out the length of AB
Give your answer to 3 significant figures

Answer 1

Given : ABC is a right angled triangle , AC=16cm , Angle C=90 , Size of angle B:size of angle A=3:2

To find : length of AB

Solution:

AC = 16 cm

∠C = 90°

∠A + ∠B = 90°

∠B  : ∠A  = 3 : 2

∠B  = (3/(3 + 2) ) * 90° = 54°

∠A  = (2/(3 + 2) ) * 90° = 36°

Cos 36°  =  AC/AB

=> AB  = AC/Cos36°

Cos36°  = (√5  + 1 )/4

=> AB = 16 * 4 / (√5  + 1 )

=> AB =  16(√5  - 1 )

=> AB = 16(2.236 - 1)

=> AB = 16(1.236)

=> AB =  19.776  cm

length of AB =  19.776  cm

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