A triangle is defined by the three points: a=(7, 10), b=(9, 10), and c= (5, 6). How do I determine all three angles in the triangle (in radians)?

We haven't gone over this yet in class and I'm lost. What equation(s) am I even suppose to use? How would I reason something like this out and know which steps to take?

1 Answer
Nov 12, 2017

See below.

Explanation:

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I have marked the triangle in a more conventional way. The first thing we need to do, is find the length of the sides a , b and c. We can do this by using the Distance Formula. The Distance Formula states, where d is the distance, that:

d=(x2x1)2+(y2y1)2

So:

a=(95)2+(106)2=32=42

b=(75)2+(106)2=20=25

c=(97)2+(1010)2=4=2

We now know all 3 sides, but since we don't know any angles, we will have to use the Cosine Rule.

The Cosine Rule states that:

a2=b2+c22bccos(A)

Angle A:

(42)2=(25)2+(2)22(25)(2)cos(A)

32=20+485cos(A)

cos(A)=3220485=885=55

A=cos1(cos(A))=cos1(55)=2.034 radians.

We rearrange the formula for angle B.

b2=a2+c22accos(B)

Angle B:

(25)2=(42)2+(2)22(42)(2)cos(B)

20=32+4162cos(B)

cos(B)=20324162=16162=22

B=cos1(cos(B))=cos1(22)=π4

Angle C:

π(π4+2.034)=0.322

So solution is:

a=42

b=25

c=2

A=2.034 radians.

B=π4 radians

C=0.322 radians

3 .d.p.