The length of BC is __ units ?
1 answer:
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Answer:
.
Step-by-step explanation:
The given circle has equation .
This is the equation that has its center at the origin with radius 4 units.
When this circle is translated seven units to the right and five units up, then the center of the circle will now be at (7,5).
The equation of a circle with center (h,k) and radius r units is .
This implies that, the translated circle will now have equation.
.
.
Answer:
1045.01 rounded to the nearest hundredth
Step-by-step explanation:
First, we can draw this out. The angle of depression is the angle formed by the object at the top and the line formed by the object at the top and the object at the bottom.
If the truck on the left is truck A and the truck on the right is truck B, with the helicopter being the circle on top, there is one 60 degree angle of depression and one 20 degree one. If we make a point at the point in the road the helicopter is straight above, and we connect the points, we can form two right triangles, as shown. If we can calculate the lengths of sides x and y, we can add them up to find the length between the two trucks.
Starting with side x, we know one angle and the side length adjacent to that angle. We want to find the length opposite that angle. One formula that encompasses this is tan(θ) = opposite/adjacent. Therefore, tan(60) = x/500
tan(60) = x/500
multiply both sides by 500 to isolate the x
tan(60) * 500 = x
x = 866.0254
Similarly, with side y, we can say that tan(20) = y/500 and
tan(20) * 500 = y
y= 181.9851
The distance between the two trucks can be shown as x+y, so x+y= 1045.01 rounded to the nearest hundredth
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