Question

Find the quantities indicated in the picture (Type an integer or decimal rounded to the nearest TENTH as needed.)

Answer 1

Remember that 3, 4 and 5 is a Pythagorean triple, since:

`3^2+4^2=5^2`

Since one side of the given right triangle has a length of 3 and the hypotenuse has a length of 5, then, the remaining leg b must have a length of 4.

Therefore:

`b=4`

The angles A and B can be found using trigonometric identities.

Remember that the sine of an angle equals the quotient of the lengths of the side opposite to it and the hypotenuse of the right triangle.

The side opposite to A has a length of 3 and the length of the side opposite to B is 4. Then:

`\begin{gathered} \sin (A)=(3)/(5) \\ \sin (B)=(4)/(5) \end{gathered}`

Use the inverse sine function to find A and B:

`\begin{gathered} \Rightarrow A=\sin ^(-1)((3)/(5))=36.86989765\ldotsº \\ \Rightarrow B=\sin ^(-1)((4)/(5))=53.13010235\ldotsº \end{gathered}`

Then, to the nearest tenth:

`\begin{gathered} A=36.9º \\ B=53.1º \end{gathered}`

Therefore, the answers are: