Question

Solve for X in the triangle. Round answer to the nearest tenth.

Answer 1

Answer: 2.6

Explanation:

Finding the right trigonometric function to use

In this problem, we have to choose between three trigonometric functions:

sine, cosine, and tangent

Each function relates the angle of a right triangle to 2 of the three sides of the triangle:

the sine of an angle is equal to the ratio of the side opposite to the angle to the hypotenuse of the triangle:
`sin(x)=(opposite)/(hypotenuse)`

`tan(x)=(opposite)/(adjacent)`

`cos(x)=(adjacent)/(hypotenuse)`

In this case, we are given the hypotenuse and need to find the side adjacent to the angle, so we will use cosine.

Calculating the adjacent side

Plugging in the values for the hypotenuse and the angle to the cosine equation, we get

`cos(58)=(x)/(5)\\x=5(cos(58))\\`

Entering into a calculator, we get x≈2.6