IF THE SIDE OPPOSITE A 45 ANGLE IN A RIGHT TRIANGLE 12.5 METERS, HOW LONG IS THE ANGLE?(ROUND THE ANSWER TO THE NEAREST TENTH)
the sides will be 12.5, 12.5, and 12.5*1.414
To find the length of the hypotenuse in a right triangle, we can use the trigonometric function sine (sin). In this case, since we are given the length of the side opposite the angle, we can use the sine function to find the length of the hypotenuse.
The sine function is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. Mathematically, it can be expressed as:
sin(angle) = opposite / hypotenuse
In this case, we know that the opposite side is 12.5 meters and we want to find the hypotenuse. Rearranging the formula, we can solve for the hypotenuse:
hypotenuse = opposite / sin(angle)
To find the angle, we need to rearrange the formula to:
angle = arcsin(opposite / hypotenuse)
Plugging in the known values, we get:
angle = arcsin(12.5 / hypotenuse)
Now, since we want to find the length of the angle, we need to use the inverse sine function (arcsin) to find the angle in radians. However, the problem asks us to round the answer to the nearest tenth.
To get the answer, we need to follow these steps:
1. Use a calculator that has the arcsin function.
2. Plug in the value of the opposite side (12.5 meters) into the formula: angle = arcsin(12.5 / hypotenuse).
3. Solve for the angle using the calculator and round the answer to the nearest tenth.
Note: Since we don't have the value of the hypotenuse, we can only find the angle in terms of the hypotenuse. To find the actual length of the angle, we need to know the length of the hypotenuse.