How do I calculate this tangent angle?

Question

http://hotmath.com/help/solutions/cpmg02/7/2/Classwork/cpmg02_7_2_Classwork_T-18_264/index.html

Thanks again.

Answer 1

Well there are two options:

1. Using a calc. Quick, but you learn nothing.

2. Using the phrase: SohCahToa

SohCahToa:
sin x = opposite/hypotenuse
cos x = adjacent/hypotenuse
tan x = opposite/adjacent

So for a)
tan 30 = x/20

b)
20 tan 30 = x >>> solving for x, simple

c)
tan b = tan 60 = 20/x
tan 60 = 20/x
x tan 60 = 20
x = 20 / tan 60

Answer 2

From the web page you linked:

"Consider the triangle shown. Suppose we want to find the length of the opposite leg when we know the length of the adjacent leg is 20. The tangent value of a specific angle (in this case, 30) is always constant (that is, it does not change if the side lengths increase or decrease). Thus, regardless of the lengths of the sides of the triangle, the value

"tan 30" is the same and simply represents a number in the equation below.

a) Tan A = . Complete the equation using this definition with the x and 20 from the figure above: tan 30 = ?

b) Solve the equation for x. Do not find the value of tan 30 until the end of the problem. Use Fraction Busters as necessary.

c) Suppose you use B to solve for x. Complete the following equation and solve for x. Your result should be the same as in part (b). tan 60 = ?"
-----------------------------------------------------------

The tangent of an angle is simply the ratio of the opposite leg divided by the adjacent leg. The number you get will always be the same, no matter how big the RIGHT triangle is.

a)
Just remember: Tangent of Angle = O / A
O means Opposite
A means Adjacent

Tan A = (Opposite leg) / (Adjacent leg)

Tan A = x / 20

A = 30 degree's

..so...

Tan 30 = x / 20

b) You can use Google to find the tangent..etc...
For example, go to Google and type in the search box:

what is tan 30 degrees

or it is easier if you type:

tan 30 degrees

Google gives the answer for Tan 30 degrees as:

"tan(30 degrees) = 0.577350269"

...so...

Tan 30 degrees = 0.577350269

Solve for x

Tan 30 = x / 20

..move the side with x to the left...

x / 20 = Tan 30

multiply both sides by 20

x = 20 * Tan 30

x = 20 * 0.577350269

x = 11.5470054

...I don't know why they ask you to solve for the Tan at the end of this question... Do you?

c) Using angle B

Tan B = Opposite / Adjacent

Tan B = 20 / x

B = 60 degrees... so...

Tan 60 = 20 / x

switch x to the left side...

20 / x = Tan 60

invert both sides and get....

x / 20 = 1 / Tan 60

multiply both sides by 20...the 20 cancels the other 20 under the x on the left side....and you get....

x = 20 / Tan 60

Using Google to find Tan 60 degrees...
tan(60 degrees) = 1.73205081
Tan 60 = 1.73205081

substitute Tan 60 with decimal number equivalent....

x = 20 / 1.73205081

x = 11.5470054

This value matches the value for x in the above steps. Good!

By the way, you can use Google to make many other calculations... multiplying... and complex math formulas too.

I hope this helps..and I hope you learn !!!!

Math is VERY important. Enjoy !! ....

...and more importantly...

Jesus loves you !!!!!!!

Answer 3

Finish writing the equation for tangent:
tan30° = x/20
x = 20tan30°
Without resorting to a calculator, we know from geometry that the hypotenuse of this triangle is 2x, so
x^2 + 20^2 = (2x)^2
3x^2 = 400
x^2 = 400/3
x = 20/√3
so
tan30° = 20/20√3 = 1/√3 = 0.57735

Answer 4

sinθ/cosθ=tanθ

sinθ=1/2
cosθ=sqr(3)/2

tan30=(1/2)/sqr(3)/2
tan30=1/sqr3=sqr(3)/3