Question

#3 list the angles of each triangle in order from smallest to biggest

Answer 1

Statement Problem: (3)

List the angles of the triangle in order from smallest to largest.

Solution:

First, let's use the Cosine Rule to find the angle B;

`\begin{gathered} b^2=a^2+c^2-2ac\cos B \\ 2ac\cos B=a^2+c^2-b^2 \\ \cos B=(a^2+c^2-b^2)/(2ac) \end{gathered}`

Where;

`\begin{gathered} a=3,b=2.9,c=3.1 \\ \cos B=(3^2+3.1^2-2.9^2)/(2(3)(3.1)) \\ \cos B=(9+9.61-8.41)/(18.6) \\ \cos B=(10.2)/(18.6) \\ \cos B=0.5484 \\ B=\cos ^(-1)(0.5484) \\ B=56.74 \\ B=57^o \end{gathered}`

Also, let's use the Cosine Rule to find the angle A;

`\begin{gathered} a^2=b^2+c^2-2bc\cos A \\ \cos A=(b^2+c^2-a^2)/(2bc) \end{gathered}`
`\begin{gathered} \cos A=(2.9^2+3.1^2-3^2)/(2(2.9)(3.1)) \\ \cos A=(8.41+9.61-9)/(17.98) \\ \cos A=(9.02)/(17.68) \\ A=\cos ^(-1)(0.5102) \\ A=59.32 \\ A=59^o \end{gathered}`

Lastly, let's use the sum of angles in a triangle theorem to get the third angle, Angle C;

`\begin{gathered} \angle A+\angle B+\angle C=180^o \\ \angle C=180^o-59^o-57^o \\ \angle C=64^o \end{gathered}`

Hence, the angles of the triangle from the smallest to the largest are;

`\angle B,\angle A,\angle C`

Angle B,

Angle A,

Angle C