Question

n a right triangle, the length of side b is 17 inches and the measure of angle B is 38 degrees. Use trigonometry to find the length of the hypotenuse.Make sure you draw this diagram and set up the correct ratio. Enter the number only, without the units. Round to the nearest tenth (one decimal place)

Answer 1

Using the sine function and the given angle of 38 degrees, we can calculate the length of the hypotenuse of the right triangle by dividing 17 inches by the sine of 38 degrees.

Step-by-step explanation:

To find the length of the hypotenuse in a right-angled triangle when one side and an angle are known, we use trigonometric ratios. Considering side b as the opposite side to angle B, we can use the sine function, which is defined as the ratio of the opposite side over the hypotenuse (sin(B) = opposite/hypotenuse).

In this case, we have: sin(38°) = 17/hypotenuse. To find the hypotenuse, we rearrange the formula: hypotenuse = 17/sin(38°). By using a calculator to find the sine of 38 degrees and dividing 17 by that number, we can determine the length of the hypotenuse.

It is also important to remember that in trigonometry, the ratios such as sine, cosine, and tangent have no units and relate the sides of a right triangle. Through the use of these trigonometrical relationships, we can solve various problems relating to right triangles.