Working with Ratios in Right Triangles

Working with Ratios in Right Triangles

Tuesday Feb 9, 2021

Today you will need 2 things

1) A calculator

2) Trig table (which you can find in Google Classroom - save it as an image so you can keep it up on your screen)

Your work today is actually impossible to do without these two things so you really need to have them.

Using your Trig Table

When a rocket is launched, it climbs 50 feet for every 13 feet it travels horizontally. Estimate the rocket's launch angle

*You'll submit your answer on the next slide when you're ready*

Open Ended

What's the rocket's launch angle?

Solution

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

• Calculate

   $50\div13=3.846$  

• 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.

Open Ended

Given this diagram, and using angle A as your reference angle, calculate the ratio of adjacent / hypotenuse. Write your answer as a/h=

a/h = 0.96

• adjacent = 24

• hypotenuse = 25

•  $\frac{a}{h}=\frac{24}{25}=0.96$  

Open Ended

Given this diagram, and using angle A as your reference angle, calculate the ratio of opposite / hypotenuse. Write your answer as o/h=

o/h = 0.28

• opposite = 7

• hypotenuse = 25

•  $\frac{o}{h}=\frac{7}{25}=0.28$  

Open Ended

Given this diagram, and using angle A as your reference angle, calculate the ratio of opposite / adjacent. Write your answer as o/a =

o/a = 0.292

• opposite = 7

• adjacent = 24

•  $\frac{o}{a}=\frac{7}{24}=0.292$  

Open Ended

 $\frac{a}{h}=0.96,\ \ \frac{o}{h}=0.28,\ \ \frac{o}{a}=0.292$  

Using your Trig Table, estimate the measures of the two acute angles

Find the acute angles

•  $\frac{a}{h}=0.96$  

•  $\frac{o}{h}=0.28$  

•  $\frac{o}{a}=0.292$  

• 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  $80\degree$  

To find AB

• 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:  $a=0.940\times8.5$  

•  $a=7.99\ \rightarrow\ a=8$  

Find DE

• 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

Open Ended

Find DE. Write your answer as DE =

DE = 7.2 units

If you got it wrong, go back and try it again now that you know the answer.

A solution will be posted tomorrow morning