1. The lengths of the legs of a right triangle are given. Find the length of the hypotenuse If the legs: 15 yd and 20 yd the hypotenuse is:
13mm
10yds
25 mm
25 yds
The length of the hypotenuse of a right triangle can be found using 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 lengths of the legs are given as 15 yards and 20 yards.
Using the Pythagorean theorem:
hypotenuse^2 = leg1^2 + leg2^2
hypotenuse^2 = 15^2 + 20^2
hypotenuse^2 = 225 + 400
hypotenuse^2 = 625
Taking the square root of both sides to find the length of the hypotenuse:
hypotenuse = sqrt(625)
hypotenuse = 25
Therefore, the length of the hypotenuse is 25 yards.
Find the Length of the missing leg if you have 1 leg- 24mm and the hypotenuse of 25 mm. What is the other leg? *
10mm
10 yds
7 mm
7 yds
To find the length of the missing leg of a right triangle, we can again use the Pythagorean theorem.
Given that one leg is 24 mm and the hypotenuse is 25 mm, we can denote the missing leg as x mm.
Using the Pythagorean theorem:
hypotenuse^2 = leg1^2 + leg2^2
25^2 = 24^2 + x^2
625 = 576 + x^2
49 = x^2
Taking the square root of both sides to find the length of the missing leg:
x = sqrt(49)
x = 7
Therefore, the length of the missing leg is 7 mm.
Two angles are complementary if the sum of their angles are*
*
90 °
180°
360°
Two angles are complementary if the sum of their angles is 90°.
Which of the following could not be the side lengths of a triangle? *
9, 5, 5
4, 9, 5
4, 3,6
To determine if a set of numbers could be the side lengths of a triangle, we need to apply the triangle inequality theorem. According to this theorem, for a triangle with side lengths a, b, and c, the sum of the lengths of any two sides must be greater than the length of the third side.
Let's check the options:
1. 9, 5, 5
The sum of the two shorter sides is 5 + 5 = 10. Since 10 is greater than the longest side (9), these lengths could be the side lengths of a triangle.
2. 4, 9, 5
The sum of the two shorter sides is 4 + 5 = 9. Since 9 is equal to the longest side (9), these lengths could be the side lengths of a degenerate triangle (a triangle with collinear points).
3. 4, 3, 6
The sum of the two shorter sides is 3 + 4 = 7. The sum of the two shorter sides is not greater than the longest side (6). Therefore, these lengths could not be the side lengths of a triangle.
So, the set of numbers that could not be the side lengths of a triangle is 4, 3, 6.
If a triangle has 2 angles that each measure 75 degrees, what is the measure of the third angle? *
Imagen sin título
25 °
40 °
30 °
other?
The sum of the angles in a triangle is always 180 degrees.
Given that two angles in the triangle each measure 75 degrees, let's denote the measure of the third angle as x degrees.
The sum of the three angles is given by the equation: 75 + 75 + x = 180
Simplifying the equation: 150 + x = 180
Subtracting 150 from both sides: x = 30
Therefore, the measure of the third angle is 30 degrees.
If a triangle has 2 angles that each measure 75 degrees, what is the measure of the third angle?
25 °
40 °
30 °
other?