Question

Which of the following describes how to calculate the value of x?

Answer 1

First option sin20 times eight

Explanation:

This is a right triangle, and we have the hypotenuse 8 (the side opposite to the angle of 90°), and angle of 20°, and we want to calculate the opposite leg (x) to the angle of 90°. The trigonometric function that relates the opposite leg to an angle and the hypotenuse is sine:

`sin 20^(\°)=(Opposite leg)/(Hypotenuse)`

Replacing the values:

`sin 20^(\°)=(x)/(8)`

Solving for x: Multiplying both sides of the equation by 8:

`sin20^(\°).8=(x)/(8).8\\ sin20^(\°).8=x\\x=sin20^(\°).8`

Answer: We can calculate x with sin20 times eight

Answer 2

Option 1

Explanation:

Given in the picture is a right triangle

One leg is x and hypotenuse is 8

The angle opposite leg x is given as 20 degrees

Recall the formula for trignometric ratio

`sin t =(opposite side)/(hypotenuse)`

Here opposite side of 20 is x and hypotenuse =8

Hence
`sin 20 =(x)/(8) \\8 sin20=x`

So option I is right.