a right triangle contains a 25 angle. if me leg is of length 5 inches what is the length of the hypotenuse
Ah, we've got a right triangle that's a comedian! Well, if you've got a 25-degree angle and a leg that measures 5 inches, let me unleash my mathematical wit. We can make a side-splitting calculation using the sine function!
The sine of the 25-degree angle is equal to the opposite side (which is the unknown hypotenuse length) divided by the hypotenuse side. But fear not, I'll spare you from the intricate math. Putting it all together, the length of the hypotenuse would be approximately 12.09 inches.
So, there you have it, my friend! The punchline to the length of the hypotenuse in this right triangle is roughly 12.09 inches. Enjoy your mathematical comedy routine!
To find the length of the hypotenuse in a right triangle, we can use the Pythagorean theorem.
Step 1: Identify the given information:
- One leg of the triangle has a length of 5 inches.
- One angle in the triangle is 25 degrees.
Step 2: Recall the Pythagorean theorem:
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). Mathematically, it can be written as:
c^2 = a^2 + b^2
Step 3: Calculate the length of the other leg:
Since we know the angle is 25 degrees, we can use trigonometric ratios to find the length of the other leg. In this case, we can use the sine ratio since we know the opposite side (5 inches) and the hypotenuse (which is what we are trying to find).
Using the sine ratio: sin(angle) = opposite/hypotenuse
sin(25) = 5/hypotenuse
Solving for the hypotenuse:
hypotenuse = 5/sin(25)
Step 4: Calculate the length of the hypotenuse:
Using a calculator, evaluate the expression for the hypotenuse:
hypotenuse ≈ 11.55 inches
Therefore, the length of the hypotenuse is approximately 11.55 inches.
To find the length of the hypotenuse of a right triangle, we can use the trigonometric function called the sine.
In this case, the given angle is 25 degrees, and one of the legs is 5 inches.
The sine of an angle is defined as the ratio of the length of the opposite side to the length of the hypotenuse. Therefore, we can set up the following equation:
sin(25 degrees) = opposite / hypotenuse
By rearranging the equation, we get:
hypotenuse = opposite / sin(25 degrees)
Substituting the given values, we have:
hypotenuse = 5 inches / sin(25 degrees)
Now, we can use a scientific calculator or an online trigonometric calculator to calculate the sine of 25 degrees. Let's assume that the sine of 25 degrees is approximately 0.423.
hypotenuse = 5 inches / 0.423
Calculating the division, we find:
hypotenuse ≈ 11.82 inches
Therefore, the length of the hypotenuse is approximately 11.82 inches.
Which leg is the "me" leg?
I assume you mean ONE of the legs that are not the hypotenuse.
The right triangle must have angles of 25, 65 and 90 degrees in this case.
You need to specify whether the 5 inch leg is the shortest or longest leg. The two legs can be either
5 and (5tan25= 2.33) or 5 and (5tan 65 = 10.72).
Those will lead to two greatly different hypotenuse lengths.