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

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

Answer:

           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:

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