To find the length of the diagonal support (x), we can use the cosine function:
cos(65 degrees) = adjacent / hypotenuse
cos(65 degrees) = x / 25 feet
Using a calculator, we can find the cosine of 65 degrees:
cos(65 degrees) ≈ 0.4226
Now we can solve for x:
0.4226 = x / 25
x = 0.4226 * 25
x ≈ 10.6 feet
Therefore, the length of a diagonal support (x) is approximately 10.6 feet.
A 25-foot-long footbridge has two diagonal supports that meet in the center of the bridge.
Each support makes a 65 angle with a short vertical support.
A diagram shows the footbridge, the diagonal supports and the vertical supports create two right triangles. At the top of the diagram a horizontal line is shown and labeled 25 feet. The two right triangles are shown below this horizontal line.The two longest legs of both right triangles touch at the center of the footbridge.The shortest leg of both right triangles represents the vertical support on each end of the footbridge. The hypotenuse of both right triangles form the diagonal supports that meet at the center of the footbridge. The full length of the footbridge is 25 feet. The vertical supports are not labeled. Each diagonal support is labeled X. A 65-degree-angle is formed between the short vertical support and the diagonal support on each end of the bridge.
What is the length x of a diagonal support, to the nearest tenth of a foot?
x= blank feet
1 answer