Question

A right triangle is given. The base of the triangle is labeled as 8.5 and the hypotenuse is labeled as x. The angle�� is between the height and the hypotenuse and measures 40 degrees. Determine the value for x.

1) 6.5
2) 7.1
3) 11.1
4) 13.2

Answer 1

To find the hypotenuse x in a right triangle with a base of 8.5 units and an angle of 40 degrees, you use the cosine function. Calculate x as 8.5 / cos(40°), which gives x ≈ 11.1 units.

Step-by-step explanation:

To determine the value for x, the length of the hypotenuse in a right triangle where the base is 8.5 units and the angle between the height and hypotenuse is 40 degrees, one can utilize the trigonometric functions, specifically the cosine function. The cosine of an angle in a right triangle is equal to the adjacent side (base in this case) divided by the hypotenuse (x):

cos(40°) = 8.5/x

Using this equation, we can solve for x:

• x = 8.5 / cos(40°)

To find the value of cos(40°), you can use a calculator set to degree mode. Plug in the numbers to obtain the hypotenuse value:

• x ≈ 11.1

Therefore, the length of the hypotenuse x is approximately 11.1 units.