Find the value of x. (Note: the line passing through the center of the circle is a diameter)
2 answers:
We know that
<span>The measure of the interior angle is the half-summit of the arcs that comprise it and its opposite.
see the attached figure with letters to better understand the problem
measure of the arc ADCB is equal to 180 degrees
arc DC=180-(arc BC+arc AD)----> arc DC=180-(60+70)---> 50</span>°
<span>arc DC=50</span>°
<span>so
</span>∡x=(1/2)*[arc AB+arc DC]---> (1/2)*[180+50]----> ∡ x=115°
<span>
the answer is
x=115</span>°
<span>The measure of the interior angle is the half-summit of the arcs that comprise it and its opposite.
see the attached figure with letters to better understand the problem
measure of the arc ADCB is equal to 180 degrees
arc DC=180-(arc BC+arc AD)----> arc DC=180-(60+70)---> 50</span>°
<span>arc DC=50</span>°
<span>so
</span>∡x=(1/2)*[arc AB+arc DC]---> (1/2)*[180+50]----> ∡ x=115°
<span>
the answer is
x=115</span>°
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Pictures always help; see the one I've attached for reference.
Call the first vector (from HQ to the supply drop) u and the second vector (from supply drop to medics) v. We then want to find w, the vector from the medics to HQ, which corresponds to the vector -(u + v). (This is because u + v is the vector pointing from HQ to the medics; we're talking about the one in the opposite direction.)
Write the vectors in horizontal/vertical component form:
u = (125 km) (cos 235º x + sin 235º y) = (-71.70 x - 102.39 y) km
v = (75 km) (cos 110º x + sin 110º y) = (-25.65 x + 70.48 y) km
Why these angles?
- "55 degrees south of west" is 235º; due west is 180º from the positive horizontal axis, and you add 55º to this
- "20 degrees west of north" is 110º; due north is 90º, so add 20º to this
Add the vectors:
u + v = (-97.35 x - 31.92 y) km
Multiply by -1 to get the vector w:
w = -(u + v) = (97.35 x + 31.92 y) km
The distance covered by this vector is equal to its magnitude:
||w|| = √((97.35 km)^2 + (31.92 km)^2) = 102.45 km
The direction <em>θ</em> is given by
tan<em>θ</em> = (31.92 km)/(97.35 km) ==> <em>θ</em> = 18.15º
