ABC is a right angled triangle in which ∠ABC = 90° and ∠ACB = 60°. BC is produced to D such that ∠ADB = 45°. If CD = 30 cm, what are the lengths of AB and BC?

Asked by akifmohd007 | 3rd Jan, 2020, 12:06: PM

Expert Answer:

ABC is a right angled triangle such that right angled at B and angle ACB is 60o. BC is produced to D such that angle ADB is 45o and CD is 30 cm.
To find the lengths of AB and BC.

I n space triangle A B C comma space angle A B C equals 90 degree space a n d space angle A C B equals 60 degree
rightwards double arrow angle B A C equals 30 degree
A s space angle A C B equals 60 degree space a n d space B minus C minus D
rightwards double arrow angle A C D equals 120 degree
rightwards double arrow angle C A D equals 15 degree space... space open parentheses because space angle A D B equals 45 degree close parentheses
I n space triangle A B D comma space angle A D B equals 45 degree space a n d space angle B A D equals 45 degree
rightwards double arrow A B equals B D equals B C plus 30 space... space left parenthesis i right parenthesis
I n space triangle A B C comma
tan space 60 degree equals fraction numerator A B over denominator B C end fraction
rightwards double arrow A B equals square root of 3 B C space... space left parenthesis i i right parenthesis
F r o m space left parenthesis i right parenthesis space a n d space left parenthesis i i right parenthesis comma space w e space h a v e
B C plus 30 equals square root of 3 B C
rightwards double arrow open parentheses square root of 3 minus 1 close parentheses B C equals 30
rightwards double arrow B C equals 40.98 space c m
rightwards double arrow A B equals 70.98 space c m

Answered by Renu Varma | 7th Jan, 2020, 10:50: AM