Two angles of a triangle are 45º each and its longest side is 12cm. Find the length of one of the other sides

Chikezieikennahenry

4 years ago

that 450 supposed to be written like this ..45⁰ so using Pythagoras theorem .. you have
sin 45⁰= x/12 ..where x is the other side of the angle .. and 12 the longer side ,and the angle 45⁰ lieing on the opposite angle of the triangle.... taking sine rule ...which is opposite/ ajacent
.....sin45⁰. =x/12 =0.7071*12= 8.485 converting to surd form you have ..6√2........

Rhoda21

2 years ago

Let's denote the two angles of the triangle as A, B, and C, with C being the angle opposite the longest side. We know that angles A and B are both 45 degrees.

In a triangle, the sum of all angles is always 180 degrees. So, we can find angle C by subtracting the sum of angles A and B from 180 degrees:

C = 180 - A - B
C = 180 - 45 - 45
C = 90 degrees

Now, we can use the Law of Sines to find the length of one of the other sides.

The Law of Sines states that in any triangle, the ratio of the length of a side to the sine of the angle opposite that side is constant. Mathematically, it can be written as:

a/Sin(A) = b/Sin(B) = c/Sin(C)

Let's denote the length of the longest side as c = 12 cm. We want to find the length of one of the other sides, which we'll denote as a.

Using the Law of Sines, we can write the following equation:

a/Sin(A) = c/Sin(C)

Substituting the known values:

a/Sin(45) = 12/Sin(90)

Since Sin(45) = Sin(90) = 1, the equation simplifies to:

a/1 = 12/1
a = 12 cm

Therefore, the length of one of the other sides of the triangle is 12 cm.