Answer:
707.9
Step-by-step explanation:
Let find some missing angles using the triangle interior theorem,
- The triangle is split up into 3 triangles, (2 right triangles and 1 scalene triangle.)
- Let find the missing angle of the triangle on the top.
- Using triangle interior theorem, the missing angle is 48.
We can use law of sines to find the missing side since we know.
- We know the angle opposite of the side we trying to find, 42
- We know a side and it opposite side, 518 and 48.
Let y represent the top triangle vertical side.
[tex] \frac{y}{ \sin(42) } = \frac{518}{ \sin(48) } [/tex]
[tex]y = \frac{518}{ \sin(48) } \times \sin(42) [/tex]
[tex]y = 466.4[/tex]
- Know let find the missing side of the bottom
- The missing angle near the top triangle right angle is 90 degrees.
- Using triangle interior theorem, the .missing angle is 65.
We can law of sines since we know a side and the angle opposite of it, and we are trying to find a side and we know an angle opposite of it.
Let z represent the missing side of the bottom triangle vertical side,
[tex] \frac{518}{ \sin(65) } = \frac{z}{ \sin(25) } [/tex]
[tex] \frac{515}{ \sin(65) } \times \sin(25) = z [/tex]
which is about
[tex]241.5[/tex]
Y and Z both add to X so add the vertical side together
[tex]466.4 + 241.5 = 707.9[/tex]
So
[tex]x = 707.9[/tex]
