Triangle 90
A triangle has sides of 6 cm, 4.5 cm, and 7.5 cm. What are the sizes of its angles?
Final Answer:
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Dr. Math
To find the angles of a triangle with sides 6 cm, 4.5 cm, and 7.5 cm, we can use the Law of Cosines. This law relates the lengths of the sides of a triangle to the cosine of one of its angles. The formula is:
Where:
- a, b, c are the lengths of the sides,
- A is the angle opposite side a .
Let:
- a = 7.5 cm (opposite angle A ),
- b = 6 cm (opposite angle B ),
- c = 4.5 cm (opposite angle C ).
Substitute the values:
Substitute the values:
Substitute the values:
The sum of the angles in a triangle is 180° :
The angles of the triangle are approximately:
- A = 90° ,
- B ≈ 53.13° ,
- C ≈ 36.87° .
cos(A) = b2 + c2 - a22bc
Where:
- a, b, c are the lengths of the sides,
- A is the angle opposite side a .
Step 1:
Identify the sidesLet:
- a = 7.5 cm (opposite angle A ),
- b = 6 cm (opposite angle B ),
- c = 4.5 cm (opposite angle C ).
Step 2:
Use the Law of Cosines to find angle Acos(A) = b2 + c2 - a22bc
Substitute the values:
cos(A) = 62 + 4.52 - 7.522 · 6 · 4.5
cos(A) = 36 + 20.25 - 56.2554
cos(A) = 054 = 0
A = cos-1(0) = 90°
Step 3:
Use the Law of Cosines to find angle Bcos(B) = a2 + c2 - b22ac
Substitute the values:
cos(B) = 7.52 + 4.52 - 622 · 7.5 · 4.5
cos(B) = 56.25 + 20.25 - 3667.5
cos(B) = 40.567.5 = 0.6
B = cos-1(0.6) ≈ 53.13°
Step 4:
Use the Law of Cosines to find angle Ccos(C) = a2 + b2 - c22ab
Substitute the values:
cos(C) = 7.52 + 62 - 4.522 · 7.5 · 6
cos(C) = 56.25 + 36 - 20.2590
cos(C) = 7290 = 0.8
C = cos-1(0.8) ≈ 36.87°
Step 5:
Verify the anglesThe sum of the angles in a triangle is 180° :
A + B + C = 90° + 53.13° + 36.87° = 180°
Final Answer:
The angles of the triangle are approximately:
- A = 90° ,
- B ≈ 53.13° ,
- C ≈ 36.87° .
Tips for related online calculators
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Cosine rule uses trigonometric SAS triangle calculator.
See also our trigonometric triangle calculator.
Try conversion angle units angle degrees, minutes, seconds, radians, grads.
Cosine rule uses trigonometric SAS triangle calculator.
See also our trigonometric triangle calculator.
Try conversion angle units angle degrees, minutes, seconds, radians, grads.
You need to know the following knowledge to solve this word math problem:
algebraarithmeticplanimetricsgoniometry and trigonometryUnits of physical quantitiesGrade of the word problem
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