Answer:
The measure of the angle formed from the line from each lamppost to Bob is 41°
Step-by-step explanation:
* Lets explain how to solve the problem
- Bob is standing 25 feet from a lamppost that is to his left and 30 feet
from a lamppost that is to his right
- Assume that Bob is standing at point B, the position of the left
lamppost is L and the position of the right lamppost is R
∴ Bob , with the two lampposts formed Δ BLH
∵ The distance between Bob and the left lamppost is 25 feet
∴ The length of side BL = 25 feet
∵ The distance between Bob and the right lamppost is 30 feet
∴ The length of side BH = 30 feet
∵ The distance between the two lamppost is 20 feet
∴ The length of side LH = 20 feet
* Lets use the cosine rule to find the angle between Bob and the
two lampposts (∠ LBH)
- The cosine rule in Δ ABC is:
[tex]cos(A)=\frac{b^{2}+c^{2}-a^{2}}{2bc}[/tex], where a is the side
opposite to angle A and b , c are the other two sides
- In Δ BLH
∵ The side LH is opposite to angle LBH
∵ ∠LBH is the angle between Bob and the lampposts
∴ [tex]cos(LBH)=\frac{(LB)^{2}+(HB)^{2}-(LH)^{2}}{2(BL)(BH)}[/tex]
∴ [tex]cos(LBH)=\frac{(25)^{2}+(30)^{2}-(20)^{2}}{2(25)(30)}[/tex]
∴ [tex]cos(LBH)=\frac{3}{4}[/tex]
- To find the measure of the angle use the inverse function [tex]cos^{-1}[/tex]
∴ m∠LBH = [tex]cos^{-1}\frac{3}{4}[/tex]
∴ m∠LBH = 41°
∵ ∠ LBH represents the angle between Bob and the lampposts
∴ The measure of the angle formed from the line from each
lamppost to Bob is 41°
Answer:
41
Step-by-step explanation:
bob says the instruction is b o o t y.
