Question

Question 8

A triangle with sides of length 3, 4, and 5 is shown. What is the measure of angle B in degrees?

Answer 1

Answer: B = 36.87°

Explanation:

Since this is a right triangle, we can use trigonometry functions. From the given angle, we are given all three sides. This means we can use pretty much any function we want to. I will use the sine function, it uses the hypotenuse and the opposite side in a ratio. Then, we will isolate the B variable.

Given:

`\displaystyle sin(B)=\frac{\text{opposite side}}{\text{hypotenuse}}`

Substitute given sides:

`\displaystyle sin(B)=(3)/(5)`

The inverse of sine of both sides of the equation:

`\displaystyle sin^(-1)(sin(B))= sin^(-1)((3)/(5))`

`\displaystyle B= sin^(-1)((3)/(5))`

`\displaystyle B= 36.86989764\° \approx 36.87\°`