Question

Express tan a using x

Answer 1

Given,

An angle "a".

The total height 3+4 =7 units.

The base = x units.

To Find,

The form of tan x using x.

Solution,

We can find the solution using the following method.

The formula of tan is as follows-

tan α=$\frac{Height}{Base}$.

Here the another angle be b.

So we can say for angle b, tan b= $\frac{4}{x}$.

For angle (a+b), tan (a+b)=$\frac{3+4}{x}$=$\frac{7}{x}$.

Also tan(a+b)=$\frac{tan a+tan b}{1-tan a.tanb}$.

⇒tan(a+b)=$\frac{tan a+\frac{4}{x} }{1-tan a.\frac{4}{x} }$.

⇒$\frac{7}{x}$=$\frac{tan a+\frac{4}{x} }{1-tan a.\frac{4}{x} }$.

⇒$\frac{7}{x}$=$\frac{\frac{x(tana)+4}{x} }{\frac{x-4tana}{x} }$.

⇒$\frac{7}{x}$=$\frac{x(tana)+4 }{x-4tana}$

⇒7.(x-4tan a)=x(x.tan a +4 ).

⇒7x-28tan a = $x^{2}$tan a +4x.

⇒tan a ($x^{2}$+28)=3x.

⇒tan a = $\frac{3x}{x^{2} +28}$.

Hence, the value of tan a using x is $\frac{3x}{x^{2} +28}$.

#SPJ3

Answer 2

Answer:

tan a with respect to x can be written as $tan\;a = \frac{3x}{x^2 + 28}$

Step-by-step explanation:

Given - angle a

             height of the triangle = 3 + 4 = 7 units
             base of the triangle = x units

To find - tan x

Solution - We know that the tangent of a triangle can be expressed as $tan \; \alpha = \frac{height}{base}$

Let us assume another angle to be b.

Thus, $tan \; b = \frac{4}{x}$

Now, we can write the formula as $tan (a + b) = \frac{tan\;a + tan\;b}{1 + tan\;a\times tan\;b}$

$tan (a + b) = \frac{tan\;a + \frac{4}{x} }{1 - tan\;a\;.\frac{4}{x} } \\\frac{7}{x} = \frac{tan\;a + \frac{4}{x} }{1 - tan\;a\;.\frac{4}{x} } \\\\simplifying,\\7(x-4tan\;a) = x (x.tan\;a + 4)\\7x-28\;tan\;a = x^2\;tan\;a + 4x\\tan\; a (x^2 + 28) = 3x\\tan\;a = \frac{3x}{x^2 + 28}$

Thus, tan a with respect to x is $tan\;a = \frac{3x}{x^2 + 28}$

#SPJ2