AFM Unit 1 Triangle Trig Right Triangles Pythagorean

AFM Unit 1 - Triangle Trig

Right Triangles – Pythagorean Theorem • Solve for the missing side in the right triangles.

Right Triangle Trigonometry In a right triangle there is a relationship between the sides and the angles. You might remember SOH CAH TOA.

Locating the parts of a Right Triangle

Lesson 2: Angles of Elevation and Depression • Angles of Elevation and depression ALWAYS touch a horizontal line • Elevation means from the horizontal up • Depression means from the horizontal down.

What is true about the Angle of Elevation and the Angle of Depression?

Describe the relationship between <1 and <2.

• Ben walked upstairs to the second floor of his house and realized he left his phone at the bottom of the stairs. He is too lazy to get his phone for himself and yells to Anthony to throw it up to him. From the bottom of the stairs, the phone is thrown at a 46° angle and travels 16 ft through the air. How high are the stairs?

Andrew sees a fire on the 2 nd floor of a house. He knows the fire is 20 feet off the ground and he is 12 feet from the building. At what angle does Andrew have to hold the hose if he is 6 feet tall?

Dontae is on the roof of HHS looking for his debit card. He looks left and sees Ethan on the ground at a 32 degree angle. He looks right and sees Drew at a 62 degree angle with his stolen card. If HHS is 60 feet tall, how far does Ethan have to run to tackle Evil Drew the thief?

Warm Up • 1. There is a lighthouse on the top of a hill. A ship at sea is 12 miles from the base of the hill. If the angle of elevation tot he top of the hill is 29 o, and the angle of elevation to the top of the lighthouse is 48 o, then how tall is the lighthouse? • 2. A construction crew is building a new road up a mountain. The grade of the hill is 12 o. If the height of the mountain is 67 feet, how long will the road be?

Warm Up 1. Kayla is flying a kite and wants to know how much string she will need to be above the trees. She knows that she is 5. 5 feet tall and that the trees are 14 feet tall. If she plans on holding her kite at a 60 degree angle, then how much string does she need? 2. Find x. 8 x 32 o

Facts we need to remember •

Remember that there are several ways to show that triangles are congruent. What are they? When we are solving using the Law of Sines we need an angle and side that are opposite each other. That means that it works great for ASA and AAS.

Warm Up • In ∆ABC, b = 32, m<B = 33 and m<C = 83 o. Find c.

What about when we have SSA? • Remember that the bad word does not necessarily make congruent triangles, so when looking for the missing piece there are 3 options.

Example 1

Example 2

Example 3

works when: • you have 2 sides and the included angle (SAS) to find the 3 rd side. • You have 3 sides (SSS) and want to find an angle.

Example 1: SAS • Find side a:

Example 2: SSS • Find <A.

You try: 1. Find f. 2. Find <B if side a = 12, b=14 and c=18.

Area of a triangle • Formula: ½bh where the base and the height are always perpendicular! • What is the base and height if it is a right triangle?

Find the Area

Area of a Non-Right Triangle • So that means that if you have 2 sides and the included angle of a triangle you can use the formula: •  rea = ½ (a)(b)(sin C)