Triangle: calculate angle between raised height and angle follower

In summary, if you are looking for the angle between a raised height and an angle follower at right angles, you would first draw a line from the 90º corner to the hypotenuse bisector, then draw a line from the same 90º corner to the height line. The angle between these two lines is the angle you are looking for.
  • #1
HotPrompt
4
0
One sharp corner of a right-angled triangle is 50º. Calculate the angle between the raised height and the angle follower at right angles.
So I know that the angles are 90º, 50º and 40º. How do I find the angle between the raised height and angle follower?
View attachment 8178
 

Attachments

  • gdfgdfg.png
    gdfgdfg.png
    4.5 KB · Views: 95
  • gdfgdfg.png
    gdfgdfg.png
    4.5 KB · Views: 86
Mathematics news on Phys.org
  • #2
I don't know what you mean by "angle follower". Trying to google it I get a lot of hits on 'cams' that don't seem to have anything to do with this problem.
 
  • #3
One of the lines is angle bisector and the other is a line drawn from the 90º corner to the hypotenuse.
 
  • #4
HotPrompt said:
One of the lines is angle bisector and the other is a line drawn from the 90º corner to the hypotenuse.

The sum of the angles in a triangle is 180º.
So γ = 180º - α - β = 180º - 50º - 40º = 90º.
Its angle bisector (if that is what it is, although I kind of doubt it when looking at the drawing) would therefore be 45º. (Thinking)
 
  • #5
I have to draw a line from the 90º corner to the hypotenuse c, which fill split the triangle into bisectors. After that I have to draw a new line from the same 90º corner to the hypotenuse height line, and I have to calculate the angle between these two lines. If this makes it clearer..
View attachment 8186
I have to find the angle where green "?" is, knowing only that one corner is 50º. But since it's a right-angled triangle then we know that one of the corners is 90º.
 

Attachments

  • dfgdfg.png
    dfgdfg.png
    2.8 KB · Views: 80
  • #6
HotPrompt said:
I have to draw a line from the 90º corner to the hypotenuse c, which fill split the triangle into bisectors. After that I have to draw a new line from the same 90º corner to the hypotenuse height line, and I have to calculate the angle between these two lines. If this makes it clearer..

I have to find the angle where green "?" is, knowing only that one corner is 50º. But since it's a right-angled triangle then we know that one of the corners is 90º.

The angle $\gamma$ of 90º is split into 3 smaller angles.
We already know that the top one is 40º.
So if the new line is an angle bisector (which is not clear from the drawing), it bisects $\gamma$ into 2 angles of 45º each.
It means that the unknown angle in between is 5º.
 
  • #7
Thank you, I think I got it now!
 

FAQ: Triangle: calculate angle between raised height and angle follower

How do you calculate the angle between the raised height and the angle follower in a triangle?

The angle between the raised height and the angle follower in a triangle can be calculated using the trigonometric functions sine, cosine, and tangent. Depending on the given information, you can use the inverse sine, cosine, or tangent to find the angle.

What is the raised height in a triangle?

The raised height, also known as the altitude, is the perpendicular line from one vertex of a triangle to the opposite side. It is used to find the area of a triangle and can also be used to calculate angles in a triangle.

How does the angle follower affect the triangle?

The angle follower, also known as the angle bisector, divides an angle into two equal parts. This can be helpful in finding missing angles in a triangle, as well as finding the length of other sides if one side and two angles are known.

Can the angle between the raised height and angle follower be greater than 90 degrees?

No, the angle between the raised height and angle follower cannot be greater than 90 degrees. This is because the angle between the raised height and the base of the triangle must be less than 90 degrees, otherwise the raised height would extend outside of the triangle.

How can I use the angle between the raised height and the angle follower to find the missing side length of a triangle?

If you know the angle between the raised height and the base of a triangle, you can use trigonometric functions to find the length of the missing side. For example, if you know the angle and the length of the raised height, you can use the tangent function to find the length of the adjacent side.

Similar threads

B Why does the trigonometry of obtuse angles use ref angles?
Replies
10
Views
902
MHB Difference of angles in a triangle
Replies
4
Views
1K
B Find triangles with areas that are integers
Replies
20
Views
2K
MHB [ASK] Find the ratio of the area of triangle BCH and triangle EHD
Replies
4
Views
1K
MHB What are the angles of isosceles triangle ABC?
Replies
1
Views
972
I Help with area formula using direction cosines
Replies
3
Views
430
MHB Find the distance between points C and D if the height of the tree is 4m
Replies
1
Views
2K
MHB Find Length of Side in Right Triangle w/ 45°, 90°, and 45° Angle
Replies
2
Views
1K
MHB Can You Find the Angle in This Isosceles Triangle Problem?
Replies
1
Views
1K
MHB Acute angle of right triangles
Replies
4
Views
1K

Hot Threads

Recent Insights

Back
Top