Math Is Fun Forum

taylorn5683

Member

Registered: 2017-02-01

Posts: 10

Introduction to Trigonometry (a.k.a. sohcatoha) need help understand

For angle x:
http://www.sc.whitmoreschool.org/sec/students/classes/geometry/lesson11_files/image5A9.JPG

1. What is the sin?

2. What is the cos?

3. What is the tan?

4. What is the sec?

5. What is the csc?

6. What is the cot?

Still looking at the image above, one angle is angle x, and another is the right angle (90o). Since the angles in a triangle add up to 180o, the other angle will be 90-x. For the unlabeled angle above, the angle 90-x:

7. What is the sin?

8. What is the cos?

9. What is the tan?

10. What is the sec?

11. What is the csc?

12. What is the cot?

13. If the cos of an angle is .75, what is the csc?

14. If the cot of an angle is 7/8, what is the tan?

You have collected data on several buildings.  For each building, you are given the angle of the line of sight up to the top of the building, and the distance to the building.  Calculate the height of each building.

http://www.sc.whitmoreschool.org/sec/students/classes/geometry/lesson11_files/fig0901.JPG

15.  Building 1 Angle 71o Distance 20 meters

16. Building 2 Angle 45o Distance 10 meters

17. Building 3 Angle 20o Distance 15 meters

18. Building 4 Angle 5o Distance 47.22 meters

19. Building 5 Angle 1o Distance 500 meters

20. You have climbed to the top of a tall tree. When you get to the top, you use your clinometer to discover that the angle between the tree and the line of sight to your red lunchbox is 30o. You know you left the lunchbox 20 meters from the base of the tree. How tall is the tree? (Careful! This is a little different than the building problems!)

http://www.sc.whitmoreschool.org/sec/students/classes/geometry/lesson11_files/fig0904.JPG

please help

iamaditya

Member

From: Planet Mars

Registered: 2016-11-15

Posts: 821

Re: Introduction to Trigonometry (a.k.a. sohcatoha) need help understand

Hi taylorn5683,

Welcome to the forum.

In trigonometry, Sin of any angle of a right-angled triangle is the Opposite over the hypotenuse,
cos of any angle is the adjacent over the hypotenuse and
the tan of any angle is opposite over the adjacent.

Cosec is the inverse of sine function i.e. cosec of any angle is hypotenuse over opposite,
Sec is the inverse of cosine function i.e. sec of any angle is hypotenuse over adjacent and
cot is the inverse of tan i.e. adjacent over opposite.

So, in this figure:

sin x=4/5
cos x=3/5
tan x=4/3
cosec x=5/4
sec x=5/3
cot x=3/4

Similarly you can do that for the above angle. I leave that to you. Hope you can do.

In the next question,

The angle adjacent to base( which we generally call "theta"θ) is given and the base is given and you need to find the perpendicular. Its as easy as that.

15.θ=71°
     b=20 m
     p=?

tanθ=p/b
⇒tanθ*b=p
⇒tan(71°)*20=p
⇒2.904(20)=p
⇒58.08=p

So the height of the building is 58.08 m.

I hope you can do the rest.

For more information on trigonemetry visit:http://www.mathsisfun.com/algebra/trigo … index.html
or for video lessons you may watch Khan Academy's playlist of trigonemtry:https://www.youtube.com/watch?v=Jsiy4Tx … C1DBF770E7

Hope it helps

---

Practice makes a man perfect.
There is no substitute to hard work
All of us do not have equal talents but everybody has equal oppurtunities to build their talents.-APJ Abdul Kalam