Question

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

Answer 1

Q1 B

Q2 23.7yd

Explanation:

Solution of Q2 is in the picture

Answer 2

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!