Big Ideas Geometry Section 9.7, Exams of Geometry

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• Big Ideas Geometry Section 9.

A triangle that has no right angle

These triangles either have

3 acute angles

1 obtuse angle and 2 acute angles

Fancy word for “non-right” triangle

Given any triangle -ABC, we can find the areawith one of 3 equations

b

c

a

A

B

C

So to find the area of anytriangle, you just need two sidesand the angle that is in betweenthese sides!

Find the area of -DEF.Round to the nearest tenth.

E

D

F

d

f

e

⡰

A tool used to solve triangles

There are two ways we can write the Law ofSines

b

c

a

A

B

C

c

a

A

B

C

m∠A =

m∠B = 25°m∠C = 107°

a =

b = 15c =

We have both pieces ofinformation for B, so this willbe our anchor

Because the angles of atriangle must sum to 180°,we can find m∠A.

25° + 107° + m∠A = 180°

m∠A = 48°

c

A

B

C

m∠A =

m∠B = 25°m∠C = 107°

a

b = 15c =

All that is left is side c!

A

B

C

m∠A =

m∠B = 25°m∠C = 107°

a

b = 15c

Thus, -ABC is solved!