Question

Find the value of b. Round your answer to the nearest tenth.

The figure shows acute triangle A B C. The measure of angle B is 40 degrees. The length of side A B is 10. The length of side B C is 12. The length of side C A is b.

Answer 1

Side CA = 7.8

Explanation:

Given:

Acute angled
`\triangle ABC`.

`\angle B =40^\circ`

AB = 10

BC = 12

We can use cosine rule here to find the side AC = b

Formula for cosine rule:

`cos B = (a^(2)+c^(2)-b^(2))/(2ac)`

Where

a is the side opposite to
`\angle A`

b is the side opposite to
`\angle B`

c is the side opposite to
`\angle C`

`cos 40 = (12^(2)+10^(2)-b^(2))/(2* 12* 10)\\\Rightarrow cos 40 = (144+100-b^(2))/(240)\\\Rightarrow 0.77 = (244-b^(2))/(240)\\\Rightarrow 244-b^(2) = 0.77 * 240\\\Rightarrow 244-b^(2) = 183.85\\\Rightarrow 244-183.85 = b^(2)\\\Rightarrow b^2 = 60.15\\\Rightarrow b = 7.76`

To the nearest tenth b = 7.8