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nikdorinn [45]
2 years ago
6

Evaluate tan 30° without using a calculator by using ratios in a reference triangle. Please Explain!

Mathematics
2 answers:
mote1985 [20]2 years ago
7 0

Answer:

The value of \tan 30\degree is \frac{1}{\sqrt{3}}

Step-by-step explanation:

In triangle ABC  (figure -1)

\tan \theta =\frac{prependicular}{base}

\tan \theta =\frac{BC}{AB}

\tan 30\degree =\frac{1}{\sqrt{3}}

Hence, the value of \tan 30\degree is \frac{1}{\sqrt{3}}

Hitman42 [59]2 years ago
3 0
Tan 30 degrees would be equivalent to sin(30)/cos(30).
Sin(30) is 1/2, and cos(30) is (3)^(1/2)/2.
((1/2)/((3^1/2)/2) can be made easier to solve by taking the reciprocal of the denominator, and inverting it.
This leaves (1/2)*(2/(3^(1/2)).
The 2 in the denominator of sin(30) cancels the 2 in the numerator of cos(30).
Leaving (1/1)*(1/(3^1/2)).
Here, you can see that tan(30) equals 1/(3^(1/2)). 

In regards to triangles, sin(30) is referring to a 30 degree angle in a 1-(3)^(1/2)-2 triangle, where sin is opposite/hypotenuse, and, so, is opposite the smaller, 1, leg.
As such, cos(30) is adjacent/hypotenuse and would be adjacent to the 3^(1/2), larger, leg. The hypotenuse is the same in both instances, in order to accommodate the Pythagorean theorem. 
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