8.1 Algebra 2 Trig Lesson Day 2

8.1 Algebra 2 Trig Lesson Day 2

How do you find missing sides of a right triangle?

• Label the sides given the trig ratio

• Use Pythagorean theorem to find missing third side

• Example 1:
  In the following figure,  $\tan\left(x\right)=\frac{5}{12}$   , find the exact values  $\sin\left(x\right)$   of and  $\cos\left(x\right)$  .

• Label the sides of the triangle with  $\tan\left(x\right)=\frac{5-opposite}{12-adjacent}$  

Use Pythagorean Theorem to find the hypotenuse

•  $5^{2\ }+12^2=c^2$  

•  $169=c^2$  

•  $\sqrt{169}=13=c$  

Find  $\sin\left(x\right)\ and\ \cos\left(x\right)$  

•  $\sin\left(x\right)=\frac{5}{13}$  

•  $\cos\left(x\right)=\frac{12}{13}$  

Multiple Choice

 $Given\csc\left(x\right)=\frac{5}{4},\$ find the missing side of the triangle. Hint:  Label the triangle and find the missing side using pythagorean theorem.

•  $\sqrt{41}$  

• 3

• 4

Multiple Choice

 Given the same triangle,
find  $\tan\left(x\right)$  

•  $\frac{3}{4}$  

•  $\frac{4}{3}$  

•  $\frac{5}{4}$  

•  $\frac{3}{5}$  

Multiple Choice

Hint:  Label the triangle and use pythagorean theorem to find the missing side

• $\frac{5}{3}$

• $\frac{5}{4}$

• $\frac{4}{3}$

• $\frac{3}{5}$

Multiple Choice

Hint: Find the missing side using Pythagorean theorem.

• $\frac{4}{3}$

• $\frac{4}{5}$

• $\frac{3}{4}$

• $\frac{5}{3}$