Answer:
a) [tex]c^{2}=h^{2}+(b-x)^{2}=h^{2}+b^{2}-2bx+x^{2}[/tex]
Therefore letter B is the correct answer.
b) TP = 23.7 yards
Step-by-step explanation:
a) We can rewrite [tex](b-x)^{2}[/tex] as (b-x)(b-x), so we have a product of two binomials. We can use the FOIL method to multiply it:
[tex](b-x)(b-x)=b^{2}-bx-bx+x^{2}=b^{2}-2bx+x^{2}[/tex]
so the the Law of Cosines equation will be write as:
[tex]c^{2}=h^{2}+(b-x)^{2}=h^{2}+b^{2}-2bx+x^{2}[/tex]
Therefore letter B is the correct answer.
b) Here we can use the Law of sines.
- TP is the distance between Tyrone and the piano
- DP is the distance between Diego and the piano
- TD is the distance between Diego and Tyrone.
∠A angle between TD and TP = 65°
∠B angle between TD and DP = 77°
∠C angle between TP and DP = 180° - 77° - 65° = 38°
The equation is:
[tex]\frac{TP}{sin(B)}=\frac{TD}{sin(C)}[/tex]
[tex]\frac{TP}{sin(77)}=\frac{15}{sin(38)}[/tex]
Solving it for TP, we have:
[tex]TP=sin(77)\frac{15}{sin(38)}=23.7 yards[/tex]
I hope it helps you!
