Question

A right triangle ABC has measure of angle ABC equal to 90 degrees and measure of angle ACB equal to 65 degrees. The length of AB is 12 feet.What is the distance, in feet, that the box has to travel to move from point A to point C? a12 divided by sec 65 degrees b12 cosec 65° c12 sin 65° d12 divided by cot 65 degrees

Answer 1

We need to find the length of the hypotenuse AC of the given right triangle.

In order to do so, we can use the sine of angle ACB:

`\begin{gathered} \sin\theta=\frac{\text{ opposite leg}}{\text{ hypotenuse}} \\ \\ \text{ hypotenuse }=\frac{\text{ opposite leg}}{\sin\theta} \end{gathered}`

In this problem, we have:

`\begin{gathered} \theta=65\degree \\ \\ \text{ opposite leg }=12\text{ ft} \\ \\ \text{ hypotenuse }=AC \end{gathered}`

Thus, AC, in feet, is given by:

`\begin{gathered} AC=(12)/(\sin65\degree) \\ \\ AC=12\cosec65\degree \end{gathered}`

Answer: b) 12 cosec 65°