People from two houses 9,000 feet apart are looking up at a plane that is BETWEEN them. House 1 is west of the plane has an angl
1 answer:
The distance between the plane and house 1 is 4899.2 feet
<h3>How to determine the distance between the plane and house 1?</h3>See attachment for illustration of the question, where x represents the distance between the plane and house 1
Start by calculating the angle A using:
A = 180 - 17.5 - 18.8 ----- (angles in a triangle theorem)
This gives
A = 143.7
The distance x is then calculated using the following sine theorem
a/sin(A) = b/sin(B) = c/sin(C)
Using the parameters in the diagram, we have:
x/sin(18.8) = 9000/sin(143.7)
Multiply both sides by sin(18.8)
x= sin(18.8) * 9000/sin(143.7)
Evaluate
x = 4899.2
Hence, the distance between the plane and house 1 is 4899.2 feet
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Answer:
Hence measure of arc ACD and arc AC are 340 degrees and 160 degrees respectively.
Step-by-step explanation:
Given:
A Circle with p as center and AB and CD as 2 diameters for a circle.
To Find:
Measure of ACD, and arc AC when arc AD is 20 degrees.
Solution:
<em>As we know that , Diameter is biggest chord which passes through center of circle,</em>
<em>Hence it divides the circle into two equal parts and making center as midpoint of it</em> .
(Refer the attachment)
angle APD=20 degree or arc AD=20 degree.
So AB as diameter ,so arc DB=160 degree or BPD=160 degree as A-B-P are
and angle APD and BPC are vertical opposite angles so they are congruent BPC=20 degree
Now,
points A,C,B,D,A makes circle which measures 360 degrees.
to find ACD
measure of ACD=360-(meaure of arc AD or angle APD)
=360-20
=340 degree.
Now arc AC,
as AB is diameter with p as midpoint ,A-P-B
arc APB=180 and arc BC=20 or angle BPC=20 degrees.
For measure of arc AC= measure of arc APB- arc BC
arc AC=180-20 degrees.
arc AC=160 degrees.
