Question

13. In Fig. 16.10, BCDE is a rectangle , ED = 3.88 cm,AD= 10 cm and ZDAC = 23°35'. Calculate, without using Pythagoras' theorem, calculate the length of CD(ii) the length of AC;(iii) the size of angle AEB​

Answer 1

Given : Fig. 16.10, BCDE is a rectangle , ED = 3.88 cm,AD= 10 cm and ∠DAC = 23°35'.

To Find : calculate the length of CD

(ii) the length of AC;

(iii) the size of angle AEB​

Solution:

Sin ∠DAC  = CD/AD

=> Sin (23°35') =  CD/10

=> 0.4 = CD/10

=> CD = 4   cm

Cos ∠DAC  = AC/AD

=> Cos (23°35') = AC/10

=> 0.916 = AC/10

=> AC = 9.16    cm

BC = ED = 3.88 cm

AB  = AC - BC =  9.16 - 3.88  = 5.28 cm

Cos∠AEB = BE / AB

BE = CD = 4 cm

Cos∠AEB =  4/5.28

=> Cos∠AEB = 47.5°

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