The picture below shows a box sliding down a ramp: A right triangle ABC has measure of angle ABC equal to 90 degrees and measure of angle ACB equal to 62 degrees. The length of AB is 10 feet. What is the distance, in feet, that the box has to travel to move from point A to point C?

11.33 feet.

Step-by-step explanation:

Given that the triangle is a right triangle ABC which has measure of angle ABC equal to 90 degrees and measure of angle ACB equal to 62 degrees.

The length of AB is 10 feet, which is opposite to angle ACB = 62 degrees.

The distance, in feet, that the box has to travel to move from point A to point C can be calculated by using trigonometry ratio. Since AC is the hypothenus of the triangle.

Using SinØ = opposite/hypothenus

That is

Sin Ø = AB / AC

Where Ø = 62 degree

Substitute Ø and length AB into the formula

Sin 62 = 10/ AC

AC = 10/ sin 62

AC = 10/ 0.8829

AC = 11. 33 feet.