Trigonometric Ratios in a Right Triangle
Right triangles are identified because they have an interior angle of 90° (right angle).
In right triangles, the trigonometric ratios are satisfied. For example, the following ratios are defined as:
[tex]\sin \theta=\frac{opposite\text{ leg}}{\text{hypotenuse}}[/tex][tex]\tan \theta=\frac{\text{opposite leg}}{adjacent\text{ leg}}[/tex]Where the hypotenuse is the side opposite to the right angle.
If we use the angle A=70°:
[tex]\tan A=\frac{a}{b}[/tex]Solving for b:
[tex]b=\frac{a}{\tan 70^0}=\frac{2}{2.7475}=0.7279[/tex][tex]\sin 70^o=\frac{a}{c}[/tex]Solving for c:
[tex]c=\frac{a}{\sin 70^o}=\frac{2}{0.9397}=2.1284[/tex]Rounding to one decimal place:
b=0.7
c=2.1