Find the measures of the three angles, in radians, of the triangle with the given vertices: d(1,1,1), e(1,−5,2), and f(−2,2,7).

The measures of the three angles are 90°, 48°, and 42°.

Triangle is a polygon that has three sides and three angles. The sum of the angle of the triangle is 180 degrees.

Given

The triangle with the given vertices: d(1,1,1), e(1,−5,2), and f(−2,2,7).

The measures of the three angles, in radians.

We know the distance formula

Distance between DE will be

Distance between EF will be

Distance between DF will be

Then according to the cosine rule.

Angle D will be

Angle E will be

Then the sum of the angle of the triangle is 180 degrees.

 ∠D + ∠E + ∠F = 360°

90° + 48° + ∠F = 360°

                   ∠F = 42°

Thus the measures of the three angles are 90°, 48°, and 42°.

More about the triangle link is given below.

link

Consider triangle DEF with vertices D(1,1,1), E(1,-5,2) and F(-2,2,7).

1. Find

Then

2. Find

Then

3. Find

Then

4.

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