Question

solve this trigonometry question

Answer 1

There are many methods to Solve this problem.

Given 3tanA= 4

=> tanA = 3/4 .

=> opposite side to A / adjacent side to A = 3/4

Hypotenuse² = (opp side) ²+ ( adj side) ²

= 3²+4²

Hypotenuse = 5cm.

From this; sinA = 4/5 ,CosA = 3/5 .

Now,

2sinA-7cosA/3cosA+4

=> 2(4/5)-7(3/5) / 3(3/5) + 4

=> 8/5 - 21/5 / 9/5 + 4

=>( -13/5 )/ ( 9 + 20)/5

=> -13/5 * 5/29

=> -13/29 .

Therefore, if 3tanA=4 then value of 2sinA-7cosA/3cosA+4 is -13/29 .

Option (1) is correct.

Hope it helps you

Answer 2

3 tan A = 4
TanA = 4/3 =p/b
Using pythagoras theorem
(H)^2 = (p)^2 + (b)^2
(H)^2 = (4)^2 + (3)^2
(H)^2 = 16 + 9
(H)^2 = 25
H = root 25
H = 5 cm
Now here is the value. ....
H = 5 ; p = 4 ; b = 3

SinA = p/h = 4/5
CosA = b/h = 3/5
Now put these values in equation
2 (4/5) - 7 (3/5 ) ÷ 3 (3/5)+4
8/5 - 21/5 ÷ 9/5 + 4
(8 - 21)/5 ÷ (9+20)/5
-13/5 ÷ 29/5
-13/5 × 5/29 ( 5 is cancel by 5 )
-13/29
Correct answer is (i) -13/29
Hope this helpss you !!!!