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∘

Try calculation via our triangle calculator.


Try another example


Did you find an error or inaccuracy? Feel free to write us. Thank you!



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 - a2/2bc


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 - a2/2bc

Substitute the values:
cos(A) = 62 + 4.52 - 7.52/2 · 6 · 4.5

cos(A) = 36 + 20.25 - 56.25/54

cos(A) = 0/54 = 0

A = cos-1(0) = 90°

Step 3:

Use the Law of Cosines to find angle B
cos(B) = a2 + c2 - b2/2ac

Substitute the values:
cos(B) = 7.52 + 4.52 - 62/2 · 7.5 · 4.5

cos(B) = 56.25 + 20.25 - 36/67.5

cos(B) = 40.5/67.5 = 0.6

B = cos-1(0.6) ≈ 53.13°

Step 4:

Use the Law of Cosines to find angle C
cos(C) = a2 + b2 - c2/2ab

Substitute the values:
cos(C) = 7.52 + 62 - 4.52/2 · 7.5 · 6

cos(C) = 56.25 + 36 - 20.25/90

cos(C) = 72/90 = 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° .





Tips for related online calculators
See also our right triangle calculator.
Do you want to convert time units like minutes to seconds?
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:

Units of physical quantities:

Grade of the word problem:


 
We encourage you to watch this tutorial video on this math problem: video1   video2   video3

Related math problems and questions: