Question

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

Answer 1

Answer:

$B=sin^{-1}[(5\frac{sin65}{6})]$

Step-by-step 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

$\frac{sinB}{b}=\frac{sinC}{c}$

$\frac{sinB}{5}=\frac{sinC}{c}$

$sinB=(b)(\frac{sinC}{c})=(5).(\frac{sin65}{6})$

$B=sin^{-1}[(5\frac{sin65}{6})]$

Option D. is the answer.

Answer 2

Answer:

$d.sin^{-1}(\frac{5 sin65^{\circ}}{6})$

Step-by-step 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: $\frac{a}{sinA}=\frac{b}{sin B}=\frac{c}{sinC}$

Using sine law

$\frac{b}{sin B}=\frac{c}{sinC}$

Substitute the values then, we get

$\frac{5}{sin B}=\frac{6}{sin 65}$

Cross- multiply then we get

$5 sin65^{\circ}=6 sinB$

$sin B=\frac{5 sin65^{\circ}}{6}$

By division property of equality

$B=sin^{-1}(\frac{5 sin65^{\circ}}{6})$

Answer:$d.sin^{-1}(\frac{5 sin65^{\circ}}{6})$