Question

Bob is standing 25 feet from a lamppost that is to his left and 30 feet from a lamppost that is to his right. The distance between the two lampposts is 20 feet. What is the measure of the angle formed from the line from each lamppost to Bob? Approximate to the nearest degree.

Answer 1

41

Explanation:

bob says the instruction is b o o t y.

Answer 2

The measure of the angle formed from the line from each lamppost to Bob is 41°

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:

`cos(A)=(b^(2)+c^(2)-a^(2))/(2bc)`, 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

∴
`cos(LBH)=((LB)^(2)+(HB)^(2)-(LH)^(2))/(2(BL)(BH))`

∴
`cos(LBH)=((25)^(2)+(30)^(2)-(20)^(2))/(2(25)(30))`

∴
`cos(LBH)=(3)/(4)`

- To find the measure of the angle use the inverse function
`cos^(-1)`

∴ m∠LBH =
`cos^(-1)(3)/(4)`

∴ 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°