Answer:
Step-by-step explanation:
Triangle 1:
Problem:
Find leg [tex]a[/tex] of a right triangle if hypotenuse [tex]c=10[/tex] and angle [tex]\alpha =25^o[/tex].
Solution:
[tex]a[/tex] ≈ [tex]4.2262[/tex]
Explanation:
To find leg [tex]a[/tex] use formula:
[tex]\text{sin}(\alpha )=\frac{a}{c}[/tex]
After substituting [tex]\alpha =25^o[/tex] and [tex]c=10[/tex] we have:
[tex]sin(25^o)=\frac{a}{10}\\0.4226=\frac{a}{10}\\a=0.4226\times10\\[/tex]
[tex]a=4.2262[/tex]
Triangle 2:
Problem:
Find leg [tex]b[/tex] of a right triangle if leg [tex]a=4[/tex] and angle [tex]\alpha =20^o[/tex].
Solution:
[tex]b[/tex] ≈ [tex]10.9899[/tex]
Explanation:
To find leg [tex]b[/tex] use formula:
[tex]\text{tan}(\alpha)=\frac{a}{b}[/tex]
After substituting [tex]\alpha =20^o[/tex] and [tex]a=4[/tex] we have:
[tex]tan(20^o)=\frac{4}{b}\\0.364=\frac{4}{b}\\b=\frac{4}{0.364}\\b =10.9899[/tex]
