SOLUTION: In a ∆ABC,the foot of the perpendicular from A to BC is D. Given that tan B=4/3,cos C=15/17 and that AB=20cm, calculate without using tables (i) the length of side AC and BC

Algebra ->  Trigonometry-basics -> SOLUTION: In a ∆ABC,the foot of the perpendicular from A to BC is D. Given that tan B=4/3,cos C=15/17 and that AB=20cm, calculate without using tables (i) the length of side AC and BC       Log On


   

Question 1116856: In a ∆ABC,the foot of the perpendicular from A to BC is D. Given that tan B=4/3,cos C=15/17 and that AB=20cm, calculate without using tables (i) the length of side AC and BC
(ii) the value of sin A
Answer by greenestamps(13216) About Me  (Show Source):
You can put this solution on YOUR website!


(1) tan%28B%29+=+4%2F3 --> AD%2FBD+=+4%2F3

(2) cos%28C%29+=+15%2F17 --> CD%2FAC+=+15%2F17

In right triangle ADC, let CD = 15x and AC = 17x; then, using the 8-15-17 Pythagorean Triple, AD = 8x.

With AD = 8x, (1) tells us BD = 6x; then, using the 6-8-10 Pythagorean Triple, AB = 10x.

We are given that AB=10x is 20cm. That means AC=17x is 34cm and BC = BD+DC = 6x+15x = 21x is 42 cm.

Answers: AC = 34cm; BC = 42cm.