Working with Ratios in Right Triangles

Given the reference angle in the lower right you know the opposite = 50 and adjacent = 13

Calculate

Using your table find the $opposite\div adjacent$  column, and locate the row that closely matches your solution.

we are between two rows  $70\degree\ and\ 80\degree$  , so your angle will be somewhere between those two numbers.

adjacent = 24

hypotenuse = 25

 $\frac{a}{h}=\frac{24}{25}=0.96$  

opposite = 7

hypotenuse = 25

 $\frac{o}{h}=\frac{7}{25}=0.28$  

opposite = 7

adjacent = 24

 $\frac{o}{a}=\frac{7}{24}=0.292$  

 $\frac{a}{h}=0.96$  

 $\frac{o}{h}=0.28$  

 $\frac{o}{a}=0.292$  

All of these lie between  $10\degree$   and  $20\degree$  . Making angle A somewhere between there.

The other angle must be complementary, so it's between  $70\degree$  and  $80\degree$  

AB is the adjacent side to the reference angle

You are given the hypotenuse  $h=8.5$  

Use your table to find $\frac{a}{h}$  for  $20\degree$  (you should get 0.940)

 $\frac{a}{8.5}=0.940$  

Solve for a:  $a=0.940\times8.5$  

 $a=7.99\ \rightarrow\ a=8$  

Identify reference angle

Identify adjacent (a), opposite (o), and hypotenuse (h)

Find the correct ratio for $50\degree$ in your Trig Table

Solve

Write your answer on the following slide