Question

20 POINTS TO WHOEVER CAN ANSWER THIS QUESTION! PLZZZ?!

Main Street runs diagonally across the city as shown below. The distance from Juniper Street to Oak Street along Pine Road is 11√3 miles. (Picture below)

a) What is the distance from Spruce Road to Pine Road along Oak Street? Explain how you know.

b) What is the distance from Spruce Road to Pine Road along Main Street? Explain how you know.

Answer 1

hope this would help you

Answer 2

Answer:

a) The distance from Spruce Road to Pine Road along Oak Street is 11 miles,

b) The distance from Spruce Road to Pine Road along Main Street is 22 miles.

Step-by-step explanation:

a) Let x be the  distance from Spruce Road to Pine Road along Oak Street,

By the given diagram,

$tan 60^{\circ}=\frac{11\sqrt{3}}{x}$   ( Since, tan Ф = Perpendicular / Base )

$\sqrt{3}=\frac{11\sqrt{3}}{x}$

$x=\frac{11\sqrt{3}}{\sqrt{3}}=11$

Hence, the distance from Spruce Road to Pine Road along Oak Street is 11 miles

a) Let y be the  distance from Spruce Road to Pine Road along Main Street,

Again, by the given diagram,

$y^2=(11\sqrt{3})^2+(11)^2$  ( By the Pythagoras theorem )

$y^2=363+121=484\implies y = 22$

Hence, the distance from Spruce Road to Pine Road along Main Street is 22 miles.