Question

If the angle is 60 degrees in a right triangle and the opposite is 19, what is the adjacent

Answer 1

In a right triangle with one angle of 60 degrees, you can use the properties of trigonometric functions to find the length of the adjacent side. Given that the opposite side is 19, you can use the tangent function, which is defined as:

\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}
\]

For a 60-degree angle, the tangent value is:

\[
\tan(60^\circ) = \sqrt{3} \approx 1.732
\]

Now, we can set up the equation:

\[
\tan(60^\circ) = \frac{19}{\text{adjacent}}
\]

Substituting the value of \(\tan(60^\circ)\):

\[
\sqrt{3} = \frac{19}{\text{adjacent}}
\]

To find the adjacent, rearrange the equation:

\[
\text{adjacent} = \frac{19}{\sqrt{3}}
\]

To express this value more neatly, you can rationalize the denominator:

\[
\text{adjacent} = \frac{19 \cdot \sqrt{3}}{3}
\]

Calculating this gives:

\[
\text{adjacent} \approx \frac{19 \cdot 1.732}{3} \approx \frac{32.888}{3} \approx 10.96
\]

Therefore, the adjacent side is approximately \(10.96\).