Question

In ∆ABC, AC = 15 centimeters, m B = 68°, and m C = 24°. What is BC to two decimal places?

Answer 1

B

C

=

16.17

(

2

d

p

)

c

m

Step-by-step explanation:

In triangle ABC, side

A

C

=

15

, Angles are

∠

B

=

68

0

;

∠

C

=

24

0

and

∠

A

=

180

−

(

68

+

24

)

=

88

0

We know by sine law

A

C

sin

B

=

B

C

sin

A

or

15

sin

68

=

B

C

sin

88

or

B

C

=

15

⋅

sin

88

sin

68

=

16.17

(

2

d

p

)

c

m

Step-by-step explanation:

Answer 2

16.17 cm

Step-by-step explanation:

m∠B = 68°, m∠C = 24°, AC = 15 cm

m∠A = 180° - 68° - 24 = 88°

by sine law:

`(BC)/(\sin(A))=(AC)/(\sin(B))\\\\\\BC=(15)/(\sin\left(6\big8^o\right))\cdot \sin\left(8\big8^o\right)\\\\\\BC\approx(15)/(0.9272)\cdot 0.9994=16.168032....\\\\\\BC\approx16.17`