The students at Midtown Middle school sold flowers as a fundraiser in September and October. In October, they charged $1.50 for
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Answer:
The area of the enlarged triangle is times the original area
Step-by-step explanation:
we know that
The scale factor is equal to divide the measurement of the length side of the enlarged triangle by the the measurement of the length of the corresponding side of the original triangle
In his problem
Let
x------> the length side of the original triangle
so
2x-----> is the length of the corresponding side of the enlarged triangle
-------> that means is increasing
The scale factor squared is equal to the ratio of the area of the enlarged triangle divided by the area of the original triangle
so
Let
m-------> the area of the enlarged triangle
n------> the area of the original triangle
r-------> scale factor
we have
substitute
therefore
The area of the enlarged triangle is times the original area
Because there isnt 90 degrees angle in this triangle (triangle - starting point - point where he starts climbing- ending point) we will use cosine law to find magnitude of displacement. For cosine law we need 2 sides of triangle and angle between them which is exactly what is given.
a^2 = b^2 + c^2 - 2*b*c*cos(alpha)
after expressing values we get:
a^2 = 10000 + 1225 + 5734
a = 130,2 meters
to calculate angle we again use cosine law but now our unknown variable is angle alpha. our sides we will use are 100 meters and 130,2 meters because we need angle between them.
cos(alpha) = (b^2 + c^2 - a^2)/(2*b*c)
cos(alpha) = 0.98
alpha = 8.89 degrees
a^2 = b^2 + c^2 - 2*b*c*cos(alpha)
after expressing values we get:
a^2 = 10000 + 1225 + 5734
a = 130,2 meters
to calculate angle we again use cosine law but now our unknown variable is angle alpha. our sides we will use are 100 meters and 130,2 meters because we need angle between them.
cos(alpha) = (b^2 + c^2 - a^2)/(2*b*c)
cos(alpha) = 0.98
alpha = 8.89 degrees