Question

Can you please help me with this, I got it wrong and trying to understand why

Answer 1

Given:

side adjacent to given angle = 18 cm

angle given = 47°

Required:

Area and perimeter

Step-by-step 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

`\begin{gathered} tan\theta=(opposite)/(adjacent) \\ \\ tan47=(opposite)/(18) \\ \\ opposite=tan47*18 \\ \\ opposite\text{ =}1.0724*18=19.3032 \end{gathered}`

Now to get hypotenuse we can use cos function

`\begin{gathered} cos\theta=(adjacent)/(hypotenuse) \\ \\ cos47=(18)/(hypotenuse) \\ \\ hypotenuse=(18)/(0.68)=26.47 \end{gathered}`

We have all three sides, they are 18cm, 19.30 cm and 26.47

`Perimeter=sum\text{ }of\text{ }all\text{ }sides=18+19.30+26.47=63.77cm`
`Area=(1)/(2)* b* h=(1)/(2)*18*19.30=9*19.30=173.7cm^2`

Final answer:

Perimeter = 63.77 cm

Area = 173.7 square cm