I will give brainiest if this answer is correct :)
2 answers:
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<h3>Answer: Choice (a) in the upper left corner</h3>
Angle A = 68 degrees
Angle B = 22 degrees
Side AB = 2.9 cm
The three values are approximate
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Explanation:
a = BC = 2.7 and b = AC = 1.1 are the two legs of the right triangle.
Use the pythagorean theorem to find the length of the hypotenuse
a^2 + b^2 = c^2
2.7^2 + 1.1^2 = c^2
8.5 = c^2
c^2 = 8.5
c = sqrt(8.5)
c = 2.91547594742266
c = 2.9
The hypotenuse is c = AB = 2.9
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We then use trig ratios to find the two missing angles.
Let's say we ignore the hypotenuse and focus on the two legs of the triangle.
With respect to reference angle A, side BC is opposite and AC is adjacent
Use the tangent ratio to get
tan(angle) = opposite/adjacent
tan(A) = BC/AC
tan(A) = 2.7/1.1
tan(A) = 2.45454545454546
A = arctan(2.45454545454546)
A = 67.8336541779176
A = 68
Note: arctan is the same as inverse tangent or . Make sure your calculator is in degree mode.
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Similarly,
tan(angle) = opposite/adjacent
tan(B) = AC/BC
tan(B) = 1.1/2.7
tan(B) = 0.4074074074074
B = arctan(0.4074074074074)
B = 22.166345822082
B = 22
Or you could use the value of A to get B = 90-A = 90-68 = 22. This works because A+B = 90 as we're working with a right triangle. In other words, A and B are complementary angles.
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In summary we found
A = 68
B = 22
AB = 2.9
Tim has 56 more postcards than Paul.
Step-by-step explanation:
Total postcards boys have = 280
Let,
x = Paul's postcards
y = Shawn's postcards
z = Tim's postcards
According to given statement;
x + y + z = 280 Eqn 1
Eqn 2
Eqn 3
Putting value of y from Eqn 3 in Eqn 2
Eqn 4
Putting value of x and y from Eqn 4 and Eqn 3 in Eqn 1
Multiplying both sides by
Putting z=120 in Eqn 3
Putting y=96 in Eqn 2
Difference of Tim and Paul = 120-64 = 56
Tim has 56 more postcards than Paul.
Keywords: linear equation, substitution method
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