Why is the angle exactly 1/2 of one of the angles in the isosceles triangle

Alisa Taylor 2022-10-16 Answered
Why is the angle exactly 1/2 of one of the angles in the isosceles triangle
I'm sure there's a simple theorem that answers my question, but I'm unsure as to how to formulate the problem (not easy to describe geometry with words): It's a isosceles triangle where you draw a normal line on one of the "hypotenuse" sides, and then you make a right angled triangle out of that. My question is why is the 30 degree angle exactly 1/2 of the 60 degree angles we find in the isosceles triangle?
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Answers (1)

getrdone07tl
Answered 2022-10-17 Author has 23 answers
Step 1
Because if you have a right triangle, with acute angles α , β, then ( α + β ) = 90 .
Step 2
When α = 60 = 2 3 × 90 , then β = 90 60 = 90 ( 1 2 3 )
= 90 ( 1 3 ) = ( 1 2 ) × α .
Did you like this example?
Subscribe for all access

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

You might be interested in

asked 2022-07-27
What's an example of a true conditional statement with a true converse?
asked 2022-11-07
Direction in 3d space described with 2 values: Horizontal and Vertical (x and y) ranging the full 360 degrees (from -180 to +180), thus describing every possible view direction.
It seems fairly straight forward to me, that the angle between (0,0) and (5,0) would be 5 degrees.
But what is the angle between (0,0) and (5,5). If it was 2 points in 2d I would use Pythagoras theorem; having the difference be ( 5 2 + 5 2 ). But I don't think that would apply in 3d? How do I go about calculating the angle between these 2 directions?
asked 2022-08-02
Prove that if a line l 1 l is sent to itself under a reflection through l, then l 1 and l intersect at right angles
asked 2022-09-23
O is intersection of diagonals of the square ABCD. If M and N are midpoints of OB and CD respectively ,then A N M = ?
asked 2022-11-03
Hypotenuse and angle ratio relationship
In triangle B A C = 90, A B C: A C B = 1 : 2 and A C = 4 c m. Calculate the length of BC. I am interested in the solution using Pythagoras theorem.
asked 2022-11-20
Finding tangent for angle of right triangle
Given : Right A B C CH is altitude and A H = 2, B H = 8. Here is drawing

Find the t a n C B A
Here is how I solved the exercise: From that fact that ABC is right triangle A C 2 = A H A B (Altitude on hypotenuse theorem) \Rightarrow AC=\sqrt{2 \cdot 10}=\sqrt{20} and t a n C B A = A C A B = 2 5 10 = 5 5 .
However the answer in test is 12. I can't find my mistake.
asked 2022-08-27
Let A and B be two different points in the plane. Find the Locus of all the points C so A C B = 2 π 3 .

New questions