Triangle 90

Triangle made by 6 cm 4.5 cm and 7.5 cm. what angles does it make?

Correct answer:

α =  53.1301 °
β =  36.8699 °
γ =  90 °

Step-by-step explanation:

a=6 cm b=4.5 cm c=7.5 cm  test: c2=a2+b2 c2​=a2+b2​=62+4.52​=215​=7.5 cm c2​ = c => γ=90  ∘  sin α = a:c  α=π180°​⋅arcsin(a/c)=π180°​⋅arcsin(6/7.5)=53.1301∘=53°7′48"
β=90−α=90−53.1301=36.8699∘=36°52′12"
γ=90=90∘

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Showing 1 comment:
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:

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 sides
Let:
- 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 A
cos(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 B
cos(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 C
cos(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 angles
The 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° .





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