Question

Consider triangle ABC with m < C = 65 degrees , b = 5 and c = 6. Which option lists an expression that is equivalent to m < B? a. 6/5sin65 b. 5sin65/6 c. sin^-1(6/5sin65) d. sin^-1(5sin65/6)

Answer 1

`d.sin^(-1)((5 sin65^(\circ))/(6))`

Explanation:

We are given that a triangle ABC

`m\angle C=65^(\circ)`

`b=5 units`

`c=6 units`

We have to find that option which is equivalent to measure of B.

Sine Law:
`(a)/(sinA)=(b)/(sin B)=(c)/(sinC)`

Using sine law

`(b)/(sin B)=(c)/(sinC)`

Substitute the values then, we get

`(5)/(sin B)=(6)/(sin 65)`

Cross- multiply then we get

`5 sin65^(\circ)=6 sinB`

`sin B=(5 sin65^(\circ))/(6)`

By division property of equality

`B=sin^(-1)((5 sin65^(\circ))/(6))`

Answer:
`d.sin^(-1)((5 sin65^(\circ))/(6))`

Answer 2

`B=sin^(-1)[(5(sin65)/(6))]`

Explanation:

In a triangle ABC m∠ C = 65°, b = 5 and c = 6.

We have to find m∠ B.

When we apply sine rule in triangle ABC

`(sinB)/(b)=(sinC)/(c)`

`(sinB)/(5)=(sinC)/(c)`

`sinB=(b)((sinC)/(c))=(5).((sin65)/(6))`

`B=sin^(-1)[(5(sin65)/(6))]`

Option D. is the answer.