Answer:
b = 8√3
c = 16
Step-by-step explanation:
We cannot yet use the Pythagorean theorem because we only have one leg of the triangle
However, we can use trig identities to solve for the missing legs
I'll solve for b first so we can use the Pythagorean theorem after to find c
- We can use any of the trig identities to solve for b, but I will use the tangent identity since it involves the leg we were given
- [tex]tan(\alpha )=\frac{opposite}{adjacent}[/tex]
- Then solving for "opposite" which is our "b" will give us opposite = (adjacent)(tan(Ф))
- Plugging in our known values we get b = (8)(tan(60°)) = (8)(√3) = 8√3
Now that we have two legs of the triangle we can use the Pythagorean theorem to solve for the remaining leg, c.
- a² + b² = c² → [tex]c=\sqrt{a^2+b^2}[/tex]
- Plugging in our two legs of the triangle we get [tex]c=\sqrt{(8)^2+(8\sqrt{3} )^2}=\sqrt{64+192}=\sqrt{256}[/tex]
- c = 16
