A right triangle has a 40 degree angle. The hypotenuse is 10cm long. What is the length of the side opposite the 40 degree angle?
I got 6.4cm but not sure of how I got it.
how can you possibly not be sure?
Look at your calculation!
If the side you want is x, then
x/10 = sin 40°
To find the length of the side opposite the 40-degree angle in a right triangle, you can use the trigonometric function known as sine (sin).
In this case, the side opposite the 40-degree angle is the side you're looking for. Let's call this side "x".
Using the definition of sine, we have:
sin(40 degrees) = opposite/hypotenuse
We know that the hypotenuse is 10 cm.
Plugging in these values, we get:
sin(40 degrees) = x/10
To solve for x, we can rearrange the equation:
x = sin(40 degrees) * 10
Calculating sin(40 degrees) using a calculator, we get approximately 0.6428.
Substituting this value into the equation, we have:
x = 0.6428 * 10
Calculating this, we get:
x ≈ 6.43 cm
So, the length of the side opposite the 40-degree angle in the right triangle is approximately 6.43 cm. Rounded to one decimal place, this would be 6.4 cm, which matches your answer.
To find the length of the side opposite the 40-degree angle in a right triangle, you can use trigonometric functions. In this case, you can use the sine function.
The sine function relates the ratio of the length of the side opposite an angle to the length of the hypotenuse. It can be written as:
sin(θ) = opposite/hypotenuse
Where:
- θ represents the angle in question
- "opposite" represents the length of the side opposite the angle
- "hypotenuse" represents the length of the hypotenuse
Given that the hypotenuse is 10cm long and the angle is 40 degrees, you can set up the equation as follows:
sin(40°) = opposite/10
Now, you can solve for the length of the side opposite the 40-degree angle by rearranging the equation:
opposite = sin(40°) * 10
To find this value, you can use either a scientific calculator or a trigonometric table. Plugging the value of sin(40°) into the equation, you'll get:
opposite = 0.6428 * 10
Calculating this, you'll find that the length of the side opposite the 40-degree angle is approximately 6.43cm (rounded to two decimal places), not 6.4cm as you calculated.