First problem: draw a line segment through the vertex R and a point C on PQ such that the segment is perpendicular to PQ, thus forming an altitude of the triangle. This new segment CR, the new segment CP, and PR form a 30-60-90 right triangle, where the measure of angle PCR is 90 degrees. CR then occurs with PR in a ratio of
to 2, so
and this can be considered the height of a triangle whose base is PQ. The area is then
Second problem: the sum of the interior angles of any triangle is 180, so the measure of the missing angle must be 180 - 20 - 35 = 125 degrees. By the law of sines, the length of the missing side (call it
) satisfies
Use Heron's formula to find the area of the triangle:
where
is the area,
are the lengths of the sides, and
is the half the perimeter of the triangle. Then the area is about
square feet. Convert to square yards:
then round up to 7 square yards. At a price of $12.50 per square yard, the total price will be $87.50.
Answer:
2Pm+Pn+2qm-qn-2rm+rn
Step-by-step explanation:
3a+b+a+b = (3a+a) + (b+b) = 4a + 2b
Step-by-step explanation:
the independent variable is "Time", as this simply processes independently of any number of people present.
the dependent variable is "Number of People" as this changes depending on the time of the day.
Answer:
12
Step-by-step explanation: