161k views
2 votes
PLEASE HELP

In the proof of the Law of Cosines, the equation c^2=h^2+(b-x)^2was created using the Pythagorean theorem. Which equation is a result of expanding (b-x)^2?

A.c^2=h^2+b^2-x^2
B.c^2=h^2+b^2-2bx+x^2
C. c^2=h^2+b^2+x^2
not D

Two construction workers, Tyrone and Diego, are standing 15 yards apart, looking up at a piano hanging between the two men from a crane. Tyrone is staring at the piano with an angle of elevation of 65°, and Diego is looking up with an angle of elevation of 77°. What is the distance between Tyrone and the piano? Round the answer to the nearest tenth.

9.0 yd
16.1 yd
22.1 yd
23.7 yd

User Tang
by
7.1k points

2 Answers

3 votes

Answer:

Q1 B

Q2 23.7yd

Explanation:

Solution of Q2 is in the picture

PLEASE HELP In the proof of the Law of Cosines, the equation c^2=h^2+(b-x)^2was created-example-1
User Brechmos
by
8.2k points
1 vote

Answer:

a)
c^(2)=h^(2)+(b-x)^(2)=h^(2)+b^(2)-2bx+x^(2)

Therefore letter B is the correct answer.

b) TP = 23.7 yards

Explanation:

a) We can rewrite
(b-x)^(2) as (b-x)(b-x), so we have a product of two binomials. We can use the FOIL method to multiply it:


(b-x)(b-x)=b^(2)-bx-bx+x^(2)=b^(2)-2bx+x^(2)

so the the Law of Cosines equation will be write as:


c^(2)=h^(2)+(b-x)^(2)=h^(2)+b^(2)-2bx+x^(2)

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:


(TP)/(sin(B))=(TD)/(sin(C))


(TP)/(sin(77))=(15)/(sin(38))

Solving it for TP, we have:


TP=sin(77)(15)/(sin(38))=23.7 yards

I hope it helps you!

User AnnaSchumann
by
8.4k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories