Asked by Judy
If isosceles angles are 45, 67.5 and 67.5 with a height of 5.25" what is the length of the base?
Answers
Answered by
MathMate
We can take advantage of the symmetry of the isosceles triangle.
By cutting the isosceles triangle in two congruent triangles, each right triangle has a long leg measuring 5.25", (height, H).
The short leg is half the base, K.
Using trigonometry and the definition of tangent, tan(45/2°)=K/H.
=>
K=H*tan(22.5°)=2.187
The base is therefore, 2K, or twice 2.187.
By cutting the isosceles triangle in two congruent triangles, each right triangle has a long leg measuring 5.25", (height, H).
The short leg is half the base, K.
Using trigonometry and the definition of tangent, tan(45/2°)=K/H.
=>
K=H*tan(22.5°)=2.187
The base is therefore, 2K, or twice 2.187.
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.