Find the corresponding trigonometric ratios and remember that the hypotenuse is longer than the legs.
Yes, see solution.
Practice makes perfect
Let â–ł 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–ł 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.
