Answer:
q ≈ 15.2
p ≈ 2.5
Step-by-step explanation:
Given that:
- ∠PQR = 90°
- ∠QRP = 80°
- r = 15
We need to find the length of side q and p
Use the sine law to find out q, we have:
sin(QRP) = [tex]\frac{r}{q}[/tex]
<=> sin(80°) = [tex]\frac{r}{q}[/tex]
<=> q = [tex]\frac{r}{sin(80)}[/tex] = [tex]\frac{15}{0.98}[/tex] ≈ 15.2
Because PQR is a right triangle, so we use pytagon theorem to find p
[tex]q^{2} = r^{2} + p^{2}[/tex]
<=> [tex]p^{2} = q^{2} - r^{2}[/tex]
<=> [tex]p^{2} = 15.2^{2} - 15^{2} = 6.04 \\[/tex]
<=> p = [tex]\sqrt{6.04}[/tex] ≈ 2.5
