How do I find the base of isosceles triangle from the height and vertex angle?
Favorites|Homepage
Subscriptions | sitemap
HOME > > How do I find the base of isosceles triangle from the height and vertex angle?

How do I find the base of isosceles triangle from the height and vertex angle?

[From: ] [author: ] [Date: 16-03-07] [Hit: ]
- Draw a diagram.Drop a perpendicular from the vertex to the base.This makes two right-angled triangles.Thats the formula.b = 2 x 100 x tan(0........

Always draw a diagram (it's worth marks)

Bisect the vertex with a vertical line which is the ht -
use the half angle (a) to calculate half the base -
which will be equal to Tan (a) x ht

Height=100m
Vertex angle=0.007⁰ a = 0.0035⁰
Base=2 x 100 x tan 0.0035 = 0.0122m

-
The base angles of an isosceles triangle will always be equal and have a value of:

b=(180-v)/2 and since you know the height you can say:

tanb=h/(B/2)=2h/B so:

tan((180-v)/2)=2h/B

B=2h/tan((180-v)/2)...in this case:

B=2(100)/tan(89.9965)

B~0.0122m (you sure .007 is the vertex angle :P)

-
Draw a diagram.

height h
base b
vertex angle α

Drop a perpendicular from the vertex to the base.
This makes two right-angled triangles.

Each of these has:
one angle α/2
one side h and
the other perpendicular side b/2

From your diagram and the definition of tangent:
tan(α/2) = (b/2)/h = b/(2h)
b = 2htan(α/2)

That's the formula.
_______________________

In your example:
b = 2 x 100 x tan(0.0035⁰)
. .= 0.012m

-
If you need a formula for that, then you're doing something wrong.
Do you even know trig? This is basics. DRAW the triangle, set up a proportion and *work out* the formula.

Best wishes!

-
Height h cm; base b cm; vertex angle 2θ (2 for convenience)
then b/2 = h * tan θ,
b = 2h * tan θ,
Your example (m, not cm)
b = 200 * tan 0.0035°, = 0.0122
base is 1.22 cm
1
keywords: and,of,find,base,vertex,angle,height,from,How,do,triangle,isosceles,the,How do I find the base of isosceles triangle from the height and vertex angle?
New
Hot
© 2008-2010 http://www.science-mathematics.com . Program by zplan cms. Theme by wukong .