Find the corresponding trigonometric ratios and remember that the hypotenuse is longer than the legs.
Yes, see solution.
Practice makes perfect
Let â–³ ABC be the right triangle below.
We will find sin A and cos A by finding the following ratios.
sin A = a/c
cos A = b/c
Since â–³ ABC is a right triangle, we know that the hypotenuse is the longest side. This implies that a < c and b < c.
a < c
⇒
a/c < 1 [0.15cm]
b < c
⇒
b/c < 1
Let's substitute the corresponding trigonometric ratios into the inequalities above.
sin A = a/c < 1
⇒
sin A < 1 [0.15cm]
cos A = b/c < 1
⇒
cos A < 1
In consequence, since we picked a general right triangle, we can affirm that the values of sine and cosine for an acute angle of a right triangle are always less than 1.
