Question

Find the measure of the side of the right triangle whose length is designated by the lower case letter c. A right triangle has a vertical left leg labeled 18 meters with an opposite vertex labeled Upper A, a horizontal bottom leg with an opposite vertex labeled Upper B, and a hypotenuse that falls from left to right labeled c with an opposite vertex labeled Upper C. The measure of the angle at vertex A is 38 degrees and the measure of the angle at vertex C is 90 degrees. A B C 38 m c

Answer 1

The answer is 29,2368 m

Explanation:

In this case we have a right triangle and we know one side (in this case is the vertical side) and the measure of an angle different from the angle of 90 degrees, so we can solve this triangle, i.e. we can find the measure of any side (and of any angle too).

Remember that in a right triangle, labeled as in the question, we have that the vertical side is in fact the opposite leg of the angle A. So we have the following trigonometric ratio:

`</p><p>\sin (A)=\frac{\mbox{opposite leg}}{\mbox{hypotenuse}}=(a)/(c)</p><p>`

Solving the last equation for c we have

`</p><p>c=(18 m)/(\sin (38))</p><p>`

Using a calculator (don't forget to put the calculator in Deg mode) we have that the measure of the side c is 29,2368 m.