finding the hypotenuse for triangles with only one measure of 7.8 m and two angles with degrees of 90 and 40. The picture is a right triangle with the right angle on the bottom left(labeled S). The hypotenuse goes from the top left(making angle Q with the line going up from S) to the bottom right, connecting with to make angle R. It looks like this, but connected and there is a bottom line. S is where the right angle is. Q-40degrees

Question

finding the hypotenuse for triangles with only one measure of 7.8 m and two angles with degrees of 90 and 40. The picture is a right triangle with the right angle on the bottom left(labeled S). The hypotenuse goes from the top left(making angle Q with the line going up from S) to the bottom right, connecting with to make angle R. It looks like this, but connected and there is a bottom line. S is where the right angle is. Q-40degrees

|\
| \
S | \ R

What is the length of hypotenuse in triangle QRS. Round to the nearest tenth.

Answer 1

You could have just said:

Triangle QSR is right-angled with
angleQ=40°, and angleS = 90°

From your description I cannot tell if QS=7.8 or SR = 7.8

I will guess that SR=7.8
then sin40° = 7.8/QR
QR = 7.8/sin40 = 12.135

if QS = 7.8
then cos40 = 7.8/QR
QR = 7.8/cos40 = 10.18

Answer 2

To find the length of the hypotenuse in triangle QRS, you can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

In this case, we have the measurement of one side, which is 7.8 m. Let's label it as the side adjacent to angle Q (opposite to the right angle S).

Let's call the hypotenuse QR, which is the side opposite to angle R (the side we are trying to find).

Now, we need to find the length of the remaining side, which is the side opposite to angle Q. We can do this by using the fact that the sum of the angles in a triangle is 180 degrees. Since we have a right angle (90 degrees) and angle Q is 40 degrees, we can calculate angle R by subtracting the sum of the other two angles from 180 degrees: 180 - 90 - 40 = 50 degrees.

Now we have all the information we need to solve for the length of the hypotenuse QR.

Using the Pythagorean theorem:

QR^2 = QS^2 + RS^2

Since QS is 7.8 m and RS is the unknown, we can rearrange the equation to solve for QR:

QR^2 = 7.8^2 + RS^2

Now, let's substitute in the values:

QR^2 = 60.84 + RS^2

To find RS, we need to solve for it. Let's isolate RS^2:

RS^2 = QR^2 - 60.84

Now, we can substitute the angles and solve for RS:

RS^2 = QR^2 - 60.84
RS^2 = QR^2 - 60.84
RS^2 = (QS^2 + RS^2) - 60.84
RS^2 - RS^2 = QS^2 - 60.84
0 = QS^2 - 60.84
RS^2 = 60.84

To find the length of RS, you need to take the square root of both sides:

RS = sqrt(60.84)

RS ≈ 7.8 m

Now that we have the length of both sides (QS = 7.8 m and RS = 7.8 m), we can substitute these values back into the equation to solve for QR:

QR^2 = QS^2 + RS^2
QR^2 = 7.8^2 + 7.8^2
QR^2 = 60.84 + 60.84
QR^2 = 121.68
QR ≈ sqrt(121.68)
QR ≈ 11 m

Therefore, the length of the hypotenuse QR in triangle QRS is approximately 11 m.