Question

In ABC, m10. Find b to the nearest integer.

HINT: Use the information above to draw the
triangle

Answer 1

the value of b = 3

Step-by-step explanation:

m∠A = 53 degrees

m∠B = 14 degrees

a = 10

To get the value of b, we need an illustration of the triangle with the values given:

a = side opposite angle A

b = side opposite angle B

To get b, we will apply sine rule:

`\frac{a}{\sin\text{ A}}\text{ = }\frac{b}{\sin \text{ B}}`
`\begin{gathered} \frac{10}{\sin\text{ 53}\degree}\text{ = }\frac{b}{\sin \text{ 14}\degree} \\ \text{cross multiply:} \\ 10(\sin \text{ 14}\degree)\text{ = b(sin 53}\degree) \\ b\text{ = }\frac{10\text{ sin14}\degree}{\sin \text{ 53}\degree} \end{gathered}`
`\begin{gathered} b\text{ = }(10(0.2419))/(0.7986)=\text{ }(2.419)/(0.7986) \\ b\text{ = }3.03 \end{gathered}`

To the nearest integer, the value of b = 3