1. Trigonometric Ratios How do you use trig ratios? M2 Unit 2: Day 4

2. EXAMPLE 3 Using tangent Example 1 Find value of x in the triangle. tan 70 o = opp. adj. Write ratio for tangent of 70 o. tan 70 o x. = 40. Substitute. 40 ● tan 70 o = x Multiply each side by 40. 109.9 x Use a calculator to simplify. ANSWER x is about 110. Remember… SOHCAHTOA x 70 0 40

3. EXAMPLE 2 Find the value of x. SOLUTION Use the tangent of an acute angle to find a leg length. tan 32 o = opp. adj. Write ratio for tangent of 32 o. tan 32 o 11 = x Substitute. x tan 32 o = 11 Multiply each side by x. x = 11 tan 32 o Divide each side by tan 32 o x 11 0.6249 Use a calculator to find tan 32 o X ≈ 17.6 Simplify Example 2 Remember… SOHCAHTOA

4. Example 3: Find the value of each variable. Round decimals to the nearest tenth. Remember… SOHCAHTOA *Once you have 2 sides of a triangle, you can use the Pythagorean Theorem to find the missing third side.

5. Example 4: Find the value of each variable. Round decimals to the nearest tenth.

6. Example 5: Find the value of each variable. Round decimals to the nearest tenth.

7. Example 6: Find the area of the triangle. Round decimals to the nearest tenth. We need to know the lengths of the sides! It is a 45 o 45 o 90 o triangle! 45 o

8. Example 7: Find the area of the triangle. Write your answer in simplest radical form and find the decimal approximation to the nearest tenth. We need to know the altitude. a x 4

9. Example 8: Find the perimeter of the triangle. Round decimals to the nearest tenth. We need to use a trig ratio.

10. Example 9: Find the perimeter of the triangle. Write your answer in simplest radical form. It’s a 30 o 60 o 90 o triangle. 60 o 12

11. Example 10: Find the perimeter of the triangle. Round decimals to the nearest tenth. We need to use a trig ratio. 20 o

12.  Homework: pg 159-160 #11-19 odds pg 168 #9-12 all MAKE SURE YOU SHOW YOUR WORK AND DRAW THE DIAGRAMS!