Involving law of sines/cosines applications Involving law of sines/cosines

Quick reminder law of sines Law of cosines sin 𝐴 𝑎 = sin 𝐵 𝑏 = sin 𝐶 𝑐 𝑎 2 = 𝑏 2 + 𝑐 2 −2𝑎𝑏∙𝑐𝑜𝑠𝐴 𝑏 2 = 𝑎 2 + 𝑐 2 −2𝑎𝑐∙𝑐𝑜𝑠𝐵 𝑐 2 = 𝑎 2 + 𝑏 2 −2𝑎𝑏∙𝑐𝑜𝑠𝐶

What do we mean by applications When we talk about applications, we are talking about taking mathematical concepts, in this case the laws of sine/cosine, and applying them in real life situations.

Process to tackling application problems Read the problem fully Read the again and pull out key details Draw a picture pertaining to the key details from the problem Extract the “triangle” you’re solving for.

Example 1: John wants to measure the height of a tree. He walks exactly 100 feet from the base of the tree and looks up. The angle from the ground to the top of the tree is 33º. This particular tree grows at an angle of 83º with respect to the ground rather than vertically (90º). How tall is the tree? Round answer to the nearest tenth.

You try 1: Fire towers A and B are located 10 miles apart. Rangers at fire tower A spot a fire at 42°, and rangers at fire tower B spot the same fire at 64°. How far from the fire is tower a? round answer to the nearest tenth.

Example 2: To approximate the length of a lake, a surveyor starts at one end of the lake and walks 245 yards. He then turns 110º and walks 270 yards until he arrives at the other end of the lake. Approximately how long is the lake? Round answer to the nearest tenth.

You try 2: Two ships leave port at 4 p.m. making a 95° from the port. Ship a is headed north east traveling at 11.5 miles per hour. Ship b is headed south east traveling at 13 miles per hour. How far apart are they when dinner is served at 6 p.m.? Round answer to the nearest tenth.

Example 3: You’re on a boat travelling 50 miles on a straight path. Your friend decides to make a sharp 88° right turn and sails another 30 miles. How far are you guys from your original location? Round answer to the nearest tenth.

You try 3: A plane is flying 700 miles on a straight path. The plane turns left at 23° on a new path and goes 400 miles. How far is the plane from its original location? Round answer to the nearest tenth.

Example 4: A flagpole is situated on a hill that makes an angle of 18° with the horizontal. How tall is the flagpole if its shadow is 14 meters downhill when the angle of elevation of the sun is 31°? Round answer to the nearest tenth.

You try 4: A flagpole is leaning 15° from vertical up a hill that makes an angle of 26° with the horizontal. How tall is the flagpole if its shadow is 8 meters uphill when the angle of elevation of the sun is 42°? Round answer to the nearest tenth.

homework Assignment 9 Worksheet.

Have an enjoyable ultimate pi day!!!!!! 𝜋𝜋𝜋𝜋𝜋𝜋𝜋𝜋𝜋𝜋𝜋𝜋𝜋𝜋𝜋𝜋𝜋𝜋𝜋