Question

N triangle ABC, m∠A = 35° and m∠B = 40°, and a=9. Which equation should you solve to find b?

Answer 1

The equation is 9/sin(35) = b/sin(40) , The length of b = 10.086

Explanation:

* Lets explain how to solve the triangle

- In ΔABC

- a, b, c are the lengths of its 3 sides, where

# a is opposite to angle A

# b is opposite to angle B

# c is opposite to angle C

- m∠A = 35°

- m∠B = 40°

- a = 9 ⇒ the side opposite to angle A

* To solve the triangle we can use the sin Rule

- In any triangle the ratio between the length of each side

to the measure of each opposite angle are equal

- a/sinA = b/sinB = c/sinC

∴ The equation which used to find b is a/sinA = b/sinB

∵ a = 9 , m∠A = 35° , m∠B = 40°

∴ 9/sin(35) = b/sin(40) ⇒ by using cross multiplication

∴ b = 9 × sin(40) ÷ sin(35) = 10.086

* The length of b = 10.086

Answer 2

`(sin B)/(b) = (sin A)/(a)` should be used to find b.

Explanation:

We are given that in a triangle ABC, ∠A = 35°, ∠B = 40° and side a = 9 and we are to find the side length b.

Now using sine rule to find b:

`(sin B)/(b) = (sin A)/(a)`

`(sin 40)/(b) = (sin 35)/(9)`

`b=(sin 40 * 9)/(sin 35)`

b = 10.1