what is the length of the sides x and y of an isocaies triangle with the vertex angle being 46?

Question

the base of the triangle is 10

Answer 1

Divide the isoceles triangle in half into 2 right triangles. The vertex angle of each is 23. The base of the right triangles is 5. By trigonometry, we know

5 = S Sin(23) or

S = 5 / Sin(23) or about 12.7965

Answer 2

isoceles triangles have a rule making x and y equal (= angles opposite them (67degrees)).
divide the triangle into 2 right triangles. divide the length of the base by 2 to get 5. You now have two right triangles. one is x, ?, and 5. The other y, ?, and 5. Use sohcahtoa (sin-opposite hypotenuse) (cosine-adjacent hypotenuse) (tangent- opposite adjacent). *****SIN, COS, and TAN ONLY WORK WITH RIGHT TRIANGLES (that have a hypotenuse) do not use them on an isoceles triangle without making it two right triangles first!*******
FAST WAY:
use sin(23) (this equals 5/x.) 5/sin(23)=x, so x=12.79652333 or 12.80 y is the same.
NOT SO FAST, BUT MORE IMPRESSIVE WAY:
divide the angle 46 in half to get 23 as the top angle and the angle next to the line is 90 degrees (the right angle). 180 minus 90 and 23 gives you the last angle, 67 degrees.
Use a calculator (make sure it is set to degrees) type in cos(angle degree here, 67). This equals 5/x. x= 5/cos(67).
x= 12.79652333 or 12.80. y is the same.

Answer 3

OK!

You can do this with trig.
If you draw a line bisecting the vertex, you will divide the isoceles triangle into two equal right triangles. The base of each will be 5.

So, use the sine function to calculate the hypotenuse (which is one of the equal sides of the isoceles triangle).

sin (46/2) = 0.39 = 5 / hypotenuse

hypotenuse= 5/0.39 = 12.8

Sides are equal, so both x and y = 12.8

Answer 4

angles are 46, 67 & 67
from the law of sines

10/sin 46=x/sin 67
x=10*sin 67/ sin 46=12.8