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The triangle ΔABC,
the sides of the triangle a=10, b=7
the angle
Solve a triangle:
- the length of the side c
Solution:
It is known that the sine formula
Sin B =
Using Sin B ≈ 0.6062 and the trigonometric table of the book "The four-valued mathematical tables" or the calculation on the smartphone/ mobile phone: function "scientific calculator" – option "DEG" – button "SIN-1" – enter "0.6062" – button ")" – on the screen "asin(0.6062)" – button "=" – on the screen "37.315"
37.315° = 37° + 0.315 • 60’ = 37°19’
Then
Using the law of sines
Answer:
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Given:
the triangle ΔABC, the sides of the triangle
a=6.3
b=6.3
Find:
the length of the side c
Solution:
Since a=b=6.3, we see that the triangle ΔABC - is isosceles.
Then
Using the law of sines
Answer:
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Given:
the triangle ΔABC
c=14
Find:
Solution:
Using the law of sines
Answer:
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the triangle ΔABC
BC=a=6
AC=b=7.3
AB=c=4.8
Find:
Solution:
It is known that the cosine formula
Cos B =
Using the calculation’s results on the scientific calculator, we find the value of the angle B
Using the formula of the law of cosines, we find the cosine of the angle C
Cos C =
=
Using the calculation’s results on the scientific calculator, we find the value of the angle C
Then the angle A
Answer:
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Given:
the triangle ΔABC
b = 4.5
Find: the angle
Solution:
Since two angles in the triangle are equal
Therefore, the two sides are equal AC=AB=b=c=4.5
Using the law of sines
we find the side BC=a
Answer:
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Given:
the triangle ΔABC, the lengths of its sides
1) a=5 , b=c=4 | 2) a=5 , b=9 , c=6 | 3) a=17 , b=15 , c=8 |
Find: whether the triangle is obtuse, right, acute
Solution:
1) Since b=c=4, we see that the triangle ΔABC - is isosceles, and therefore acute.
Cos A =
Then the angle A is
3) Using the formula of the law of cosines
Cos B =
Since the cosine of the angle B is less than zero, hence the angle B is obtuse, and the triangle ΔABC is obtuse.
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the triangle ΔABC, two angles and the side
AD = 3 m
Find: the length of all sides of the triangle ΔABC = ?
Solution:
Knowing the size of two angles in the triangle ΔABC, we find the third angle
We find the angle
Using the law of sines
AC = (3 • 1) • 2 = 6 (m)
Using the law of sines
AB =
Using the law of sines
Answer: AB ≈ 3 m, AC = 6 m, BC ≈ 4 m.
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Given:
the triangle ΔABC
three sides a = 14, b = 18,
c = 20
Find:
all the angles of the triangle ΔABC = ?
Solution:
Since the larger side lies against the larger angle, we see that using the formula of the law of cosines
Cos C =
Cos C =
Using the calculation on the scientific calculator, we find the approximate value of the angle C
Using the formula of the law of cosines
Cos B =
Cos B =
Using the calculation on the scientific calculator, we find the approximate value of the angle B
Therefore,
Answer:
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Given:
the triangle ΔEKP, the side and two angles
EP = 0.75
Find: the side of the triangle PK = ?
Solution:
Using the law of sines
Sin 115° = Sin (180° - 65°) = Sin 65°
Then
Answer: PK ≈ 1.61.
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Given:
the triangle ΔABC, two sides and the angle
b = 18, c = 12
Find: solve the triangle - determine the values of the side and two angles
(a,
Solution:
Using the formula of the law of cosines
a =
Using the formula of the law of cosines
Cos C =
Cos C =
Using the calculation on the scientific calculator, we find the approximate value of the angle C
Therefore,
Answer: a ≈ 13.8 ;
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