Given:
side adjacent to given angle = 18 cm
angle given = 47°
Required:
Area and perimeter
Explanation:
To find area and perimeter we will have to find the sides of the triangle
We have side adjacent to given angle
To get opposite side we can use tan function
[tex]\begin{gathered} tan\theta=\frac{opposite}{adjacent} \\ \\ tan47=\frac{opposite}{18} \\ \\ opposite=tan47\times18 \\ \\ opposite\text{ =}1.0724\times18=19.3032 \end{gathered}[/tex]
Now to get hypotenuse we can use cos function
[tex]\begin{gathered} cos\theta=\frac{adjacent}{hypotenuse} \\ \\ cos47=\frac{18}{hypotenuse} \\ \\ hypotenuse=\frac{18}{0.68}=26.47 \end{gathered}[/tex]
We have all three sides, they are 18cm, 19.30 cm and 26.47
[tex]Perimeter=sum\text{ }of\text{ }all\text{ }sides=18+19.30+26.47=63.77cm[/tex][tex]Area=\frac{1}{2}\times b\times h=\frac{1}{2}\times18\times19.30=9\times19.30=173.7cm^2[/tex]
Final answer:
Perimeter = 63.77 cm
Area = 173.7 square cm
