Answer:
• m∠A=52.5°
,• m∠B=37.5°
,• c=23.3
Explanation:
Given the right triangle below:
(a)∠A
• The side length ,opposite angle A ,=18.5
,• The side length ,adjacent to angle A ,=14.2
From trigonometrical ratios:
[tex]\begin{gathered} \tan A=\frac{BC}{AC} \\ \implies\tan A=\frac{18.5}{14.2} \\ A=arctan(\frac{18.5}{14.2}) \\ m\angle A=52.5\degree \end{gathered}[/tex]The measure of angle A is 52.5°.
(b)∠B
• The side length ,opposite angle A ,=14.2
,• The side length ,adjacent to angle A ,=18.5
From trigonometrical ratios:
[tex]\begin{gathered} \tan B=\frac{AC}{BC} \\ \implies\tan B=\frac{14.2}{18.5} \\ B=arctan(\frac{14.2}{18.5}) \\ m\angle B=37.5\degree \end{gathered}[/tex]The measure of angle B is 37.5°.
(c)To find the length of c, apply the Pythagorean theorem.
[tex]\begin{gathered} c=\sqrt{a^2+b^2} \\ c=\sqrt{18.5^2+14.2^2}=\sqrt{543.89} \\ c\approx23.3 \end{gathered}[/tex]Thus:
• m∠A=52.5°
,• m∠B=37.5°
,• c=23.3
