In the triangle 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 =20 cm, Calculate without using tables (i) the lengths of sides AC and BC.(ii) the value of sin A.
length of sides AC and BC
in triangle ABD
(4x)^2 + (3x)^2 = (20)^2
on solving we get
x = 4
similarly
we get y = 2
therefore AC = 17 y
17 * 2 = 34 cm and
BC = 3x + 15 y = 42 cm
now to find sin A
USE FORMULA OF
SIN A = SIN ( A1 + A2)
= SIN A1COS A2 + COSA1SINA2
on solving we get
sin A = 84/85
in triangle ABD
(4x)^2 + (3x)^2 = (20)^2
on solving we get
x = 4
similarly
we get y = 2
therefore AC = 17 y
17 * 2 = 34 cm and
BC = 3x + 15 y = 42 cm
now to find sin A
USE FORMULA OF
SIN A = SIN ( A1 + A2)
= SIN A1COS A2 + COSA1SINA2
on solving we get
sin A = 84/85