Question

If2/3=cos find value of 4+4tanA

Answer 1

cos = 2/3

Hence, cos = adjacent/hypo = 2/3

Hence, (opposite)^2 = (hypo)^2 - (adjacent)^2
opposite = √(9 - 4)
opposite = √5

Hence sin = √5/3. ( since, sin= opposite/hypo)

4+4tan = 4(1 + tan)
= 4(1 + sin/cos)
= 4[1 + (√5/3)/(2/3)]
= 4 (1 + √5/2)
= 4 [(2+√5)/2]
= 4 [(2+ 2.23)/2] or 2(2+√5)
= 2 (4.23) or 4 + √5
= 8.46 or 4 + √5

There u go....
Hope it helped

Answer 2

$\huge\boxed{\texttt{\fcolorbox{Red}{aqua}{Hey Mate!!!!}}}$

$<b>$
If cos A = 2/3 = Base(B)/Hypotenuse(H)

So we can calculate Perpendicular (P)

Hence
$p = \sqrt{h {}^{2} - b {}^{2} } \\ p = \sqrt{3 {}^{2} - 2 {}^{2} } \\ p = \sqrt{9 - 4} \\ p = \sqrt{5}$
Now we can calculate
tan A = Perpendicular (P)/Base(B)
$= \frac{ \sqrt{5} }{2}$
Now put the value in
4 + 4 tanA
$= 4 + 4 \times \frac{ \sqrt{5} }{2} \\ = 4 + 2 \sqrt{5} \\ = 4 + 2 \times 2.236 \\ = 4 + 4.472 \\ = 8.472$
$\large{\red{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\underline{\underline{\underline{Hope\:it\:helps\: you}}}}}}}}}}}}}}}$