Draw the diagram. By similar triangles, her distance x East is
x/10 = 25/65 = 5/13
x = 50/13
Her distance y North is
y/15 = 60/65 = 12/13
y = 120/13
So her distance z from Culver City is
z^2 = (50/13)^2 + (15 - 120/13)^2
z = 25/√13 = 6.93 miles
Maria just moved to a new part of the state, and she decides to take her car for a spin to see the area. Maria’s starting point is Culver City. She drives directly toward River City, located 25 miles East and 60 miles North of Culver City. After driving for 10 miles, she turns and heads due South for 15 miles, then stops to fill up her gas tank. How far away is Maria from River City?
4 answers
where did 65 come from?
the triangle with sides 25 and 60 is just a scaled-up version of a 5-12-13 right triangle. The hypotenuse is 65.
CR = 25+60i = 65mi[22.6o].
V1 = 10mi[22.6o] CW.
V2 = 15mi[180o] CW.
V1+V2 = 10[22.6]+15[180] = (10*sin22.6+15*sin180)+(10*cos22.6+15*cos180)i
V1+V2 = 3.84-5.77i = 6.93mi[-34o] = 6.93mi[326o] CW from Culver City.
D = 65[22.6]+6.93[326-180]. 326-180 = 146o.
D = (65*sin22.6+6.93*sin146)+(65*cos22.6+6.93*cos146)i
D = 28.9+54.3i.
D = sqrt(28.9^2+54.3^2) = ___ miles from River City.
V1 = 10mi[22.6o] CW.
V2 = 15mi[180o] CW.
V1+V2 = 10[22.6]+15[180] = (10*sin22.6+15*sin180)+(10*cos22.6+15*cos180)i
V1+V2 = 3.84-5.77i = 6.93mi[-34o] = 6.93mi[326o] CW from Culver City.
D = 65[22.6]+6.93[326-180]. 326-180 = 146o.
D = (65*sin22.6+6.93*sin146)+(65*cos22.6+6.93*cos146)i
D = 28.9+54.3i.
D = sqrt(28.9^2+54.3^2) = ___ miles from River City.
1 answer