Let ABC be an isosceles triangle with AB = AC and ∠BAC=30°. Side AB and the median AD contain points Q and P respectively (point
s P and Q are not at point A) in such a way that PC=PQ. Find m∠PQC.
1 answer:
Answer:
15°
Step-by-step explanation:
Since P is on the median of ΔABC, it is equidistant from points B and C as well as from C and Q. Thus, points B, C, and Q all lie on a circle centered at P. (See the attached diagram.)
The base angles (B and C) of triangle ABC are (180° -30°)/2 = 75°. This means arc QC of the circle centered at P has measure 150°. The diameter of circle P that includes point Q is defined to intersect circle P at R.
Central angle RPC is the difference between arcs QR and QC, so is 180° -150° = 30°. Inscribed angle RQC has half that measure, so is 15°. Angle PQC has the same measure as angle RQC, so is 15°.
Angle PQC is 15°.
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Given: We have the given figure through which we can see
LK=16,
KJ=10,
LM=24,
MN=15
To Find: Whether KM || JN and the reasoning behind it.
Solution: Yes, KM || JN because
Explanation:
For this solution, we use the concept of Similar Triangles.
Now, KM || JN if ΔLKM ~ ΔLJN (i.e., if ΔLKM is similar to ΔLJN).
Now, ∠MLK=∠NLJ
To prove similarity of the two triangles, we have to show that the sides are proportional. In other words, LK:KJ = LM:LN
which is true as both sides simplify to
Thus, we see that ΔLKM ~ ΔLJN (i.e., if ΔLKM is similar to ΔLJN).
Therefore, KM || JN.
To come to the reasoning, notice that
In other words,
Answer:
Landscaping Company will charge $80 for Neighbor yard.
Step-by-step explanation:
Given:
Charges of Mr. Jones = $52
Length of Mr. Jones yard = 65 feet
Width of Mr. Jones yard = 40 feet
Now we will find the area of Mr. Jones yard.
Yard is basically in rectangular form.
Hence we can;
Area of yard is equal to product of length of the yard and width of the yard.
Framing in equation we get;
Area of Mr. Jones Yard =
Now Mr. Jones was charged $52 for a yard having Area 2600 sq. ft.
So we will find the per sq. ft charge applied by the company.
Per sq. ft charge will be equal to Charges of Mr. Jones divided by Area of Mr. Jones Yard.
Framing in equation form we get;
Per sq. ft charge =
Hence the Landscaping company charge Mr. Jones at $0.02 per sq.ft.
Now Given:
Length of Neighbor yard = 80 ft.
Width of Neighbor yard = 50 ft.
We need to find the Charges on Neighbor based on charges applied on Mr. Jones.
First we will find the Area of Neighbors yard we get;
Area of Neighbors yard =
Charges of Neighbor yard will be equal to charges Landscaping company for per sq. ft multiplied by area of Neighbors yard.
Framing in equation form we get;
Charges of Neighbor yard =
Hence Landscaping Company will charge $80 for Neighbor yard.