- My name is Emily and I am going to tour the city! Help me figure out the lengths and angles of different objects in the city using trigonometry.
- Here we have a window and we are trying o the angle of depression from the window. The height of the building is 15 ft tall and the object below is 17 ft away. Here we use the inverse of sine. Sine-1 = 15/17. The angle of depression is 62 degrees.
- x
- 17 ft
- x
- 15 ft
- 37
- x
- If we look here we are trying to find the height of the light. The length from the light to the bench is 5 ft and the angle from the bench to the post is 37 degrees. We are going to use cosine of 37= x/5. The height of the light is 4 ft.
- 5 ft
- The height from the second floor window is 8 ft tall and the hypotenuse is 10 ft long. To find the width let’s use Pythagorean theorem. 8^2 plus b^2 =10^2. So this means B = 6. The width of the building is 6 ft.wide.
- Let’s see how wide this building is!!!
- 8 ft
- b
- 10 ft
- 7 ft
- Ooo look at this staircase let’s see the width of these. So the length of this triangle is 7ft and the angle of elevation is 68 degrees. To find the width ground floor length we will have to use tan68 = 5/x. If we solve this the width of the triangle will be 2.8ft.
- x
- 68
- oh look it's a fire station I wonder what the length would be of this building if we leaned a ladder to the top of the building. The ladder is 12 ft leaning towards the top of the building which has an angle of depression of 36 degrees. To find the length we would use sine 36= x/12. After we solve this we know the fire station 's length is 7.1 ft.
- 36
- 12 ft
- 36
- x
- We are all done, I loved exploring this city and getting to find out new things, I hope you liked it too bye!!!

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