Find [tex]\tan 30^\circ[/tex] and [tex]\tan 45^\circ[/tex] using the 45-45-90 triangle theorem and 30-60-90 triangle theorem.

t an 3 0 o = 2 a 3 ​ ​ 2 a ​ ​ = 2 a ​ ⋅ a 3 ​ 2 ​ = 3 ​ 1 ​ ⋅ 3 ​ 3 ​ ​ = 3 3 ​ ​ t an 4 5 o = a 2 ​ a ​ = 2 ​ 1 ​ ⋅ 2 ​ 2 ​ ​ = 2 2 ​ ​

Answered by Anonymous | 2024-06-10

The trigonometric ratio ,
tan 30 degrees = √(3) and tan 45 degrees = 1.
According to the 45-45-90** triangle theorem**,
In an isosceles right triangle, the two legs are congruent and the hypotenuse is equal to the leg times the √2.
Therefore,
in a 45-45-90 triangle, tan 45 degrees is equal to 1.
Now, use the 30-60-90 triangle theorem.
In a 30-60-90 triangle,
The hypotenuse is twice as long as the shorter leg, and the longer leg is equal to the shorter leg times the **square root **of 3.
Therefore, if we let the shorter leg be 1, the longer leg is √3 and the hypotenuse is 2.
Using the definition of tangent ,
we have tan 30 degrees = opposite/**adjacent **
= (√(3)/1)
= √(3).
So tan 30 degrees = √(3) and tan 45 degrees = 1.
To learn more about** trigonometric ratios **visit:
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Answered by ankitvt811 | 2024-06-17

Using the properties of right triangles, we find that tan 3 0 ∘ = 3 3 ​ ​ and tan 4 5 ∘ = 1 . These results come from the 30-60-90 and 45-45-90 triangles, respectively. Both triangles help in determining the ratios needed for tangent values of these angles.
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Answered by Anonymous | 2024-11-03