Given: segment CD is an altitude of triangle ABC
Prove: a/sin(A) = b/sin(B)
In an Image of a Triangle ACB with b is the length between AC, a is the length between CB and c is the base length between AB. D is a point between AB at the Right angle forming DCB
Proof:
Statements:
1. segment CD is an altitude of triangle ABC
2. angle ADC and angle BDC are right angles
3. triangle ADC and triangle BCD are right angles
4. sin(A) = CD/b and sin(B) = CD/a
5. ?
6. b sin(A) = a sin(b)
7. a/sin(A) = b/sin(B)
Reasons:
1. Given
2. Definition of altitude
3. Definition of right angles
4. Definition of sine
5. Multiplication property of equality
6. Substitution property of equality
7. Division property of equality
Which statement is for number 5?
A. b = CD sin(B) and a = CD sin(A)
B. CD = b sin(B) and CD = a sin(A)
C. b = CD sin(A) and a = CD sin(B)
D. b sin(A) and CD = a sin(B)
1 answer