Step-by-step explanation:
STEP 1:
Find a length of third side.
Use the Pythagorean theorem:
[tex]leg^2+leg^2=hypotenuse^2[/tex]
STEP 2:
Use the trigonometric functions:
[tex]sine=\dfrac{opposite}{hypotenuse}\\\\cosine=\dfrac{adjacent}{hypotenuse}\\\\tangent=\dfrac{opposite}{adjacent}[/tex]
STEP 3:
Use theorem: the sum of the measures of acute angles of the right triangle is 90°.
Example:
We have the length of legs: a = 3, b = 4.
Let c = hypotenuse.
Use the Pyhagorean theorem:
[tex]c^2=3^2+4^2\\\\c^2=9+16\\\\c^2=25\to c=\sqrt{25}\\\\c=5[/tex]
Angle between a and c (β):
Use sine. Therefore b = opposite, c = hypotenuse:
[tex]\sin\beta=\dfrac{4}{5}=0.8[/tex]
look at the picture
[tex]\beta\approx37^o[/tex]
[tex]\alpha+\beta=90^o\to\alpha+37^o=90^o[/tex] subtract 37° from both sides
[tex]\alpha=53^o[/tex]
