What are the angles of isosceles triangle ABC?

  • MHB
  • Thread starter xyz_1965
  • Start date
  • Tags
    Triangle
In summary, in an isosceles triangle ABC with sides of length AC = BC = 8 and AB = 4, the angles are A = B = 75.5 degrees or 1.32 radians, and C = 29 degrees or 0.51 radians. These calculations were confirmed by a scientist.
  • #1
xyz_1965
76
0
In isosceles triangle ABC, the sides are of length AC = BC = 8 and AB = 4. Find the angles of the triangle . Express the answers both in radians, rounded to two decimal places, and in degrees, rounded to one decimal place.

Solution:

I think dropping a perpendicular line from the vertex at C gives me two congruent triangles.

cos(A) = cos(B) = 2/8 = 1/4.

arccos(1/4) = 75.5 degrees

So, angle A = angle B = 75.5 degrees, rounded to nearest one decimal place.

Angle C = 180 - 2arccos(1/4) = 29 degrees, rounded to nearest one decimal place.

I can do the same calculations in radians:

arccos(1/4) = 0.97 radians

So, angle A = angle B = 1.32 radians, rounded to two decimal places.

Angle C = pi - 2arccos(1/4) = 0.51 radians, rounded to two decimal places.

I hope to be right. The answers are not given in the back of the book for even number questions.
 
Mathematics news on Phys.org
  • #2


I can confirm that your calculations are correct. Dropping a perpendicular line from the vertex at C does indeed give two congruent triangles, making angle A and B equal. Your calculations for the angles in both degrees and radians are accurate. Keep up the good work!
 

What is an isosceles triangle?

An isosceles triangle is a triangle with two equal sides and two equal angles. The third side and angle can be different lengths and measures, but the two equal sides and angles will always be opposite each other.

How do you identify an isosceles triangle?

An isosceles triangle can be identified by its two equal sides and two equal angles. You can also use a ruler to measure the sides and a protractor to measure the angles to confirm that they are equal.

What is the formula for finding the area of an isosceles triangle?

The formula for finding the area of an isosceles triangle is (base * height) / 2. The base and height can be any of the three sides and corresponding perpendicular height, as long as they are both equal.

Can an isosceles triangle be a right triangle?

Yes, an isosceles triangle can be a right triangle. If two equal sides are the legs of the triangle and the third side is the hypotenuse, the two equal angles will be the acute angles and the third angle will be the right angle.

What are some real-life examples of isosceles triangles?

Some real-life examples of isosceles triangles include the roof of a house, the wings of an airplane, the sails of a sailboat, and the shape of a traffic cone.

Similar threads

Replies
2
Views
859
Replies
2
Views
787
  • General Math
Replies
1
Views
754
Replies
1
Views
737
Replies
1
Views
846
  • General Math
Replies
2
Views
817
  • General Math
Replies
1
Views
675
  • General Math
Replies
1
Views
710
Replies
2
Views
1K
  • General Math
Replies
4
Views
1K
Back
Top