5.
Find the length of the hypotenuse of a right triangle with legs of 20 cm and 21 cm.
41 cm
841 cm
6 cm
29 cm
6.
The length of the hypotenuse of a right triangle is 15 cm. The length of one leg is 9 cm. Find the length of the other leg.
6 cm
12 cm
17 cm
144 cm
7.
If the sail of a ship is 10 feet long and has a diagonal length of 26 feet, what is the height of the sail in feet?
29
24
17
8
5. To find the length of the hypotenuse of a right triangle, use the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the legs of the right triangle are 20 cm and 21 cm. Let's call the length of the hypotenuse "c".
Using the Pythagorean theorem, we have:
c^2 = (20 cm)^2 + (21 cm)^2
c^2 = 400 cm^2 + 441 cm^2
c^2 = 841 cm^2
Taking the square root of both sides to solve for "c", we get:
c = sqrt(841 cm^2)
The length of the hypotenuse is 29 cm.
Therefore, the answer is 29 cm.
6. Using the same process as in question 5, we can solve for the length of the other leg of a right triangle.
Given that the hypotenuse is 15 cm and one leg is 9 cm, let's call the length of the other leg "a".
Using the Pythagorean theorem, we have:
15^2 = 9^2 + a^2
225 = 81 + a^2
144 = a^2
Taking the square root of both sides to solve for "a", we get:
a = sqrt(144)
The length of the other leg is 12 cm.
Therefore, the answer is 12 cm.
7. To find the height of the sail, we can use the Pythagorean theorem, similar to the previous two questions.
Given that the length of the sail is 10 feet and the diagonal length of the sail is 26 feet, let's call the height of the sail "h".
Using the Pythagorean theorem, we have:
26^2 = 10^2 + h^2
676 = 100 + h^2
576 = h^2
Taking the square root of both sides to solve for "h", we get:
h = sqrt(576)
The height of the sail is 24 feet.
Therefore, the answer is 24.
To find the length of the hypotenuse of a right triangle, you can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
For question 5, the legs of the right triangle are given as 20 cm and 21 cm. To find the length of the hypotenuse, you can use the formula:
c = sqrt(a^2 + b^2)
where a and b are the lengths of the legs, and c is the length of the hypotenuse.
Plugging in the values, we have:
c = sqrt(20^2 + 21^2)
c = sqrt(400 + 441)
c = sqrt(841)
The square root of 841 is 29, so the length of the hypotenuse is 29 cm.
Therefore, the correct answer for question 5 is 29 cm.
For question 6, we are given the length of the hypotenuse (15 cm) and one leg (9 cm). Let's represent the other leg as a variable, x.
Again, using the Pythagorean theorem, we can set up the equation:
c^2 = a^2 + b^2
where c is the length of the hypotenuse and a and b are the lengths of the legs.
Plugging in the values, we get:
15^2 = 9^2 + x^2
225 = 81 + x^2
144 = x^2
Taking the square root of both sides, we have:
x = sqrt(144)
x = 12
Therefore, the length of the other leg is 12 cm.
Hence, the correct answer for question 6 is 12 cm.
For question 7, we are given the length of the hypotenuse (26 feet) and one leg (10 feet). Let's represent the height of the sail as a variable, h.
Using the Pythagorean theorem once again, we have:
c^2 = a^2 + b^2
Plugging in the given values, we get:
26^2 = 10^2 + h^2
676 = 100 + h^2
576 = h^2
Taking the square root of both sides, we have:
h = sqrt(576)
h = 24
Therefore, the height of the sail is 24 feet.
Thus, the correct answer for question 7 is 24.
all of these can be found using
a^2 + b^2 = c^2
where a and b are the legs, c the hypotenuse.
#7:
10^2 + b^2 = 26^2
b = 24
do the rest the same way, plugging two of the needed values.
if you get stuck, come on back and show how far you got.