I have an isosceles triangle. The base is 340cm, the two side anges are both 42deg. How long are the sides?

Answer 1

If the two side angles are 42 deg, then the remaining angle is 96 deg.

Let the two equal sides be both of length x

Apply the cosine rule

a^2 = b^2 + c^2 - 2bcCosA

340^2 = x^2 + x^2 -2x^2Cos96

115,600 = 2x^2(1 - cos96)

Solving gives x = 229 cm

Answer 2

Ok my friend.
As you said, you have an isosceles triangle.
I wanna ask you a question.
If you draw a line from the top angel to the middle of the base, what would be the angel of the intersection?
It'd be 90 degrees.
I'll assume you know it but if you don't know,I'll write the proveing procedure for your reference. you can find it after I write the solution to your question.
Now let's go back to your question:
I'm gonna ask you to draw the line.
Attach the top angel to the middle of the base.
Since you have a right angel in the intersection, actually you are having two right traingles right?
What is the base of this triangle?
yesss..... 340/2 = 170...(remember the line is intersecting the base of the isosceles in the middle point and therefore deviding it into two.)
Now you have a right triangle and you want to fin its hypotenuse.
Cos 42 = Adjacent side/ hypotenuse
=>Cos 42 = 170/ hypotenuse
=> hypotenuse = 170/Cos 42
=> hypotenuse = 228.757564cm


Now I'm gonna prove that the angel of intersection is 90 degrees. So pls pick up a pencil and follow up.
Draw your initial isosceles triangle with the angel A on top, B on the left side of the base and angel C at the right side.
Draw a line to the middle of the base and use the letter H to represent the intersection point.
Now you have devided the initial isosceles triangle into 2 triangles.
We want to prove any line drwn from the top angel to the middle of the base in isosceles triangles, make a right angel with the base.

First,I'll prove that the two triangles are equal:

1. The bases are equal.(we attached the AH line to the middle of the base so H is in the middle)
2. The initial triangle was a isosceles so the two sides are equal.
3. The angels between the base and the sides lines is 42deg in both.
So the two triangles are equal.
This means their top angel is equal too. So the line that we drew has devided the top angel into halves.

The top angel in the initial triangle was:
42 + 42 + top angel = 180 =? the top angel = 96deg
since the AH line has devided this angel into halves, so the top angel of each of the smaller triangles = 96/2 = 48deg.
take the ACH triangle.
The top angel = 48
the angel C = 42
=> 42 + 48 + angel CHA = 180
=> angel CHA = 90
therefore any line attaching the top angel of an isosceles triangel to the middle of the base, devides the top angel into two and intersects the base in a right angel.

Ok my friend.
Here was your solution.
Hope you enjoyed.
Good Luck!

We know that in a right triangle,

Answer 3

from the vertex draw perpendicular to the base
we know that the perpendicular to the base of the isosceles
triangle bisect the base
then the base divided into two parts = 340 / 2 = 170 cm
when cos 42 = 170 / side
side = 170 / cos 42
= 228.75 cm

Answer 4

I think that mant has given the best answer. Simply divide the triangle in two by drawing a line from the angle at the top to the base line, perpendicular to this line.

Answer 5

What I would do is split the triangle in two, to get two right angle triangles and then use trig.

340/2 = 170cm

cos42=170/h

h=170 / cos42

h = 228.757 cm

Answer 6

Use the formula

a/SinA = b/SinB

here we can take a= 340, A = 96 degree
b = ? , B = 42 degree

now you can calculate the value of b.

Answer 7

You could also use the sine rule to answer the question.

A = 340 cm
a = 180-(42*2) = 96
B = ?
b = 42

A/sin a = B/sin b
340/sine(96) = B/sine(42)
B = 340(SINE(42))/SINE(96)
B = (0.669)340/0.994521
B= 227.504406 / .994
b = 228.75

Answer 8

L = 170/cos(42) = 228.7576 cm

Answer 9

Do your own homework young man!!! what are the youth of today coming to--!! tut--tut--tut!!