A ladder is placed 30 inches from a wall. It touches the wall at a height of 50 inches from the ground.
2 answers:
Draw a diagram (see attachment)
we can find the length of the ladder first using pythagorean theorem then use cos⁻¹(x) to find the angle measure
or
we can use tan⁻¹(x) to find the angle measure then use cos(x) to find the hyptotonuse
I'll use the first way
alrighty, so we can find the hypotnuse by using pythagoreano therrem which can be used for right triangles
so if legs are a and b and hytponuse is c then
a²+b²=c²
so
legs are 30 and 50
30²+50²=c²
900+2500=c²
3400=c²
sqrt both sides
10√34=c
the length of the ladder is 10√34 in
ok, so we know hyptonuse is 10√34
cos=adjacent/hypotonuse
but we can use cos⁻¹(x)
cos⁻¹(30/(10√34))=x°
use your calculator
59.03≈x°
the degree measure is about 59° and the length of the ladder is 10√34 in or about 59.3in
we can find the length of the ladder first using pythagorean theorem then use cos⁻¹(x) to find the angle measure
or
we can use tan⁻¹(x) to find the angle measure then use cos(x) to find the hyptotonuse
I'll use the first way
alrighty, so we can find the hypotnuse by using pythagoreano therrem which can be used for right triangles
so if legs are a and b and hytponuse is c then
a²+b²=c²
so
legs are 30 and 50
30²+50²=c²
900+2500=c²
3400=c²
sqrt both sides
10√34=c
the length of the ladder is 10√34 in
ok, so we know hyptonuse is 10√34
cos=adjacent/hypotonuse
but we can use cos⁻¹(x)
cos⁻¹(30/(10√34))=x°
use your calculator
59.03≈x°
the degree measure is about 59° and the length of the ladder is 10√34 in or about 59.3in
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A. First let us start with the linear model.
The equation is in the form of y = m x + b
Calculating for the slope m:
m = (309,587 – 50,000) / (2007 – 1997)
m = 25,958.7
Subsituting:
y = 25,958.7 x + b
Taking x = 1997, y = 50,000. Solve for b:
50,000 = 25,958.7 (1997) + b
b = -51,789,523.9
The complete equation is therefore:
y = 25,958.7 x - 51,789,523.9
B. The exponential model has the following form:
y = a b^x
where a and b are constants
Taking x1= 1997, y1 = 50,000; x2 = 2007, y2 = 309,587
50,000 = a b^1997
309,587 = a b^2007
Combining in terms of a:
50,000 / b^1997 = 309,587 / b^2007
b^2007 / b^1997 = 309,587 / 50,000
b^10 = 6.19174
b = 1.2
Substituting:
y = a 1.2^x
Solving for a:
50,000 = a 1.2^1997
a = 3.75 x 10^-154
The complete equation is:
y = 3.75 x 10^-154 * 1.2^x
