Given the triangle $$ABC$$, whose sides are $$a = 3$$, $$b = 4$$ and $$c = 5$$, being $$x$$ the angle of the $$A$$ vertex, compute the following values:
- $$\sin (x)$$
- $$\cos (x)$$
- $$\tan (x)$$
See development and solution
Development:
First, we define how long each side of the triangle is:
$$$ \overline{AB}=5 \qquad \overline{AC}=4 \qquad \overline{BC}=3$$$
Then, once the length of every side is calculated, we proceed by computing the trigonometric ratios that have been told to:
- $$\sin (x)=\dfrac{3}{5}=0.6$$
- $$\cos (x)=\dfrac{4}{5}=0.8$$
- $$\tan (x)=\dfrac{3}{4}=0.75$$
Solution:
- $$\sin (x)=0.6$$
- $$\cos (x)=0.8$$
- $$\tan (x)=0.75$$