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Solving Triangles

The contents of this online page:

– the problems 76 - 77 are presented with examples of solutions and answers for the lesson "Solving triangles";
– the questions, how to find the solution of a triangle having used sine and cosine of an angle, are considered in the tests 78 - 81;
– the solutions, how to find the angle, the side of the triangle, are explained in the problems 82 - 85.

Problem 76.

Given:

The triangle ΔABC,

the sides of the triangle a=10, b=7

the angle A = 60°

Solve a triangle: B, C - the angles between the triangle sides,

- the length of the side c

Solution:

Answer:

B = 37°19’;

C = 82°41’; c ≈ 11

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Problem 77.

Given:

the triangle ΔABC, the sides of the triangle

a=6.3

b=6.3

C = 54°

Find: A, B - the angles between the sides of the triangle,

the length of the side c

Solution:

Answer:

A =

B = 63°; c ≈ 5.7

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Solving triangles having used the sine and the cosine of the angle

Problem 78.

Given:

the triangle ΔABC

A = 60°

B = 40°

c=14

Find: C - the angle of the triangle, the lengths of the sides a,b

Solution:

Answer:

C = 80°; a ≈ 12; b ≈ 9

***

Problem 79.

Given:

the triangle ΔABC

BC=a=6

AC=b=7.3

AB=c=4.8

Find: A, B, C - the angles of the triangle

Solution:

Answer:

A = 54°52’ ;

C = 40°52’ ;

B = 84°16’

***

Problem 80.

Given:

the triangle ΔABC

A = 30°

C = 75°

b = 4.5

Find: the angle B, the sides of the triangle a,c

Solution:

Answer:

B = 75°; a ≈ 2.3 ; c = 4.5

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Problem 81.

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:

Answer: AB ≈ 3 m, AC = 6 m, BC ≈ 4 m.

***

Problem 83.

Given:

the triangle ΔABC

three sides a = 14, b = 18,

c = 20

Find:

all the angles of the triangle ΔABC = ?

Solution:

Answer:

A ≈ 42°56’ ;

B ≈ 60°57’ ;

C ≈ 76°07’

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Problem 84.

Given:

the triangle ΔEKP, the side and two angles

EP = 0.75

P = 40°

K = 25°

Find: the side of the triangle PK = ?

Solution:

Answer: PK ≈ 1.61.

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Problem 85.

Given:

the triangle ΔABC, two sides and the angle

b = 18, c = 12

A = 50°

Find: solve the triangle - determine the values of the side and two angles

(a, B, C ) = ?

Solution:

Answer: a ≈ 13.8 ;

B ≈ 88°13’ ;

C ≈ 41°47’

***