Carlos walked 10 miles at an angle of 20 degrees north of due east. to the nearest tenth of a mile, how far east, x, is carlos from his starting point?

9.4 miles

Step-by-step explanation:

If Carlos walked 10 miles at an angle of north of due east, then how far he moved east, which is can be calculated using trigonometry.

The side opposite to the known angle is miles.

The hypotenuse of the right triangle formed is miles.

We use the cosine ratio to obtain;

miles to the nearest tenth.

answer: option a.

step-by-step explanation:

you know that the quadrilateral opqr ( a four sided figure) is inscribed in circle. this means that all its vertices are on the circle.

then, by definition, the opposite angles of the quadrilateral are supplementary, this means that the sum of their measures is 180 degrees.

you can observe in the figure that the angles ∠opq   and the angle ∠orq   are opposite, therefore:

then, can be used to d to calculate the measure of ∠opq