Answer:
[tex]IJ=14.8[/tex]
Step-by-step explanation:
In a triangle the sum of all angle measures is always 180 degrees
[tex]A+B+C=180[/tex]
[tex]2(67)+C=180[/tex]
[tex]C=46[/tex] degrees
By splitting the isosceles triangle down the middle we can calculate the base
So ∠H = 23°, ∠K = 90°, ∠J = 67°, HJ = 19
With this we can solve for half of the base. the trig function will need to use is sin, since the side opposite of ∠H will be part of the base. [tex]sin=\frac{opposite}{hypotenuse}[/tex]
now we need to rearrange the formula for what we have.
[tex]hypotenuse(sin)=opposite[/tex]
[tex]19sin(23)=7.423[/tex]
This value is only half of the base, so we need to double it
[tex]IJ=2(7.423)=14.8[/tex]
