Question

What are the values of the three trigonometric ratios for angle l, in simplest form? sin(l) = 4/5 cos(l) = 3/5 tan(l) = 4/3

Answer 1

The values of the three trigonometric ratios for angle L, in simplest form, are:

1. $sin(L)=\frac{4}{5}$
2. $cos(L)=\frac{3}{5}$
3. $tan(L)=\frac{4}{3}$

To find the values of the three trigonometric ratios for angle L, in the simplest form:

Given -

The triangle LMN is given in the question.

• The measurement of side LM is 15 units
• The measurement of side LN is 25 units
• The measurement of side MN is 20 units

As the trigonometric properties of a triangle state that the value of sin, cos, and tan for the respective angle can be written as:

• sin(L) = perpendicular / hypotenuse
• cos(L) = base / hypotenuse
• tan(L) = perpendicular / base

Using the above trigonometric properties, the value of sin(L):

• $sin(L) =\frac{20}{25} =\frac{4}{5}$

Similarly, the value of cos(L):

• $cos(L)=\frac{15}{25} =\frac{3}{5}$

And, the value of tan(L) is:

• $tan(L)=\frac{20}{15} =\frac{4}{3}$

Therefore, the values of the three trigonometric ratios for angle L, in simplest form, are:

1. $sin(L)=\frac{4}{5}$
2. $cos(L)=\frac{3}{5}$
3. $tan(L)=\frac{4}{3}$

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What are the values of the three trigonometric ratios for angle L, in simplest form?