a quarterback made 345 pass completions during one football season. if this was 60% of his attempts,how many passes did he attem
2 answers:
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Answers:
A = 120
b = 45.0
c = 33.2
Side Note: only one triangle is possible
See attached for a visual. I used GeoGebra to draw the triangle.
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Explanation:
We are given the following information
B = 35
C = 25
a = 68
We need to find the following
A, b, c
where the lower case letters represent the side lengths; the upper case letters are the angles. The angles are opposite their corresponding sides. For instance, side lowercase b is opposite angle uppercase B. The other letters are positioned the same way.
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First use the idea that for any triangle, the three angles (A,B,C) must add to 180 degrees
A+B+C = 180
Replace B and C with 35 and 25. Solve for angle A
A+35+25 = 180
A+60 = 180
A+60-60 = 180-60
A = 120
Now that we know the three angles A = 120, B = 35, C = 25, we can find the missing sides 'b' and 'c'
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We will use the law of sines to find side b
sin(A)/a = sin(B)/b
sin(120)/68 = sin(35)/b
b*sin(120) = 68*sin(35) <<--- cross multiply
b = 68*sin(35)/sin(120)
b = 45.037013350222 <<--- use a calculator; this value is approximate
b = 45.0 <<--- round to the nearest tenth
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Do the same for side c
sin(A)/a = sin(C)/c
sin(120)/68 = sin(25)/c
c*sin(120) = 68*sin(25) <<--- cross multiply
c = 68*sin(25)/sin(120)
c = 33.1838323365404 <<--- use a calculator; this value is approximate
c = 33.2 <<--- round to the nearest tenth
A = 120
b = 45.0
c = 33.2
Side Note: only one triangle is possible
See attached for a visual. I used GeoGebra to draw the triangle.
-------------------------------------------------------------
-------------------------------------------------------------
Explanation:
We are given the following information
B = 35
C = 25
a = 68
We need to find the following
A, b, c
where the lower case letters represent the side lengths; the upper case letters are the angles. The angles are opposite their corresponding sides. For instance, side lowercase b is opposite angle uppercase B. The other letters are positioned the same way.
-----------------------
First use the idea that for any triangle, the three angles (A,B,C) must add to 180 degrees
A+B+C = 180
Replace B and C with 35 and 25. Solve for angle A
A+35+25 = 180
A+60 = 180
A+60-60 = 180-60
A = 120
Now that we know the three angles A = 120, B = 35, C = 25, we can find the missing sides 'b' and 'c'
-----------------------
We will use the law of sines to find side b
sin(A)/a = sin(B)/b
sin(120)/68 = sin(35)/b
b*sin(120) = 68*sin(35) <<--- cross multiply
b = 68*sin(35)/sin(120)
b = 45.037013350222 <<--- use a calculator; this value is approximate
b = 45.0 <<--- round to the nearest tenth
-----------------------
Do the same for side c
sin(A)/a = sin(C)/c
sin(120)/68 = sin(25)/c
c*sin(120) = 68*sin(25) <<--- cross multiply
c = 68*sin(25)/sin(120)
c = 33.1838323365404 <<--- use a calculator; this value is approximate
c = 33.2 <<--- round to the nearest tenth
Answer: Choice A) 15 feet
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x = length of fourth side in quadrilateral ABCD
Have a look at the attached image I've posted. I made a chart that lines up the side lengths from largest to smallest. Note how the first two items in the bottom row are blank. We don't know these values and we don't need to find out in order to find x.
Based on the last two columns of that table, we can form the proportion below, which is then used to isolate x.
30/12 = x/6
30*6 = 12*x ... cross multiply
180 = 12*x
12*x = 180
x = 180/12 ... divide both sides by 12
x = 15
