Question

In triangle ABC , angle ABC = 90, angle CAB=x , angle BDA =y , D lie on BC , AC =17cm , BC =8 cm and BD = 6cm , Find value of 3 tan x - 2 sin y + 4 cos y

Answer 1

Given :- (Refer to image also.)

in triangle ABC,

∠ABC = 90,

∠CAB = x,

tan x = 3/4.

BC = 15 cm.

To Find :-

AB and AC = ?

Solution :-

since ∠ABC is equal to 90° . So, ∆ABC is a right angle ∆ .

in right ∆ABC now, given that,

→ ∠CAB = x,

→ tan x = 3/4.

→ BC = 15 cm.

So,

→ tan x = (Perpendicular / Base)

→ tan x = BC / AB

→ (3/4) = 15 / AB

→ 3AB = 15 * 4

→ 3AB = 60

dividing both sides by 3,

→ AB = 20 cm.

Therefore,

→ AB² + BC² = AC² (Pythagoras theorem.)

→ (20)² + (15)² = AC²

→ AC² = 400 + 225

→ AC² = 625

→ AC² = (25)²

→ AC = 25 cm.

Hence, Measures of AB and AC is 20 cm and 25 cm respectively.