1. Find the missing angle it's a long triangle 15 degrees at the top and 85 degrees at the bottom right.
2. If a right triangle has an angle that is 55 degrees, what is the measure of the third angle in the triangle?
A. 90 degrees
B. 55 degrees
C. 35 degrees
D. 180 degrees
3. Use the image to answer the question.
112 degrees 90 degrees x
Find angle x.
A. 68 degrees
B. 90 degrees
C. 158 degrees
D. 22 degrees
4. What is the measure of the exterior x? 37 degrees 32 degrees and x
5. ∠6 = 28 degrees
∠5 = 28 degrees
true or false on both
6. Angle 8 is 110 degrees and lines P and Q are parallel. Find the measure of angle 2.
7. Drag and drop the given set of measurements into the correct box to describe whether the measurements can describe the lengths of the three sides of a right triangle or not. Could be the sides of a right triangle or cannot be the sides of a right triangle.
Options are 29 in, 20 in, 21 in. 4 m 5 m 6 m. Or 63 in, 16 in, 65 in.
8. Alyissa plans to use four triangles like the one shown to form a diamond shape. 6 cm 3 cm 4 cm. For her plan to work, the triangle must be a right triangle. Determine whether the triangle is a right triangle.
The triangle ___ a right triangle.
It is or is not.
9. If a right triangle has side lengths of 9 and 12, how long is the hypotenuse?
10. If a right triangle has a leg that measures 8 inches and the hypotenuse is 12 inches, how long is the other leg? Round to the nearest tenth, if necessary.
11. Scout places his 20-foot step ladder against a house he is painting. If the bottom of the ladder is 5 feet from the base of the house, how high above the ground is the top of the ladder touching the house, to the nearest tenth of a foot?
A. 182 ft
B. 20.6 ft
C. 15.0 ft
D. 19.4 ft
12. A shortstop is standing in the base path between second and third base when she fields the ball. She is 25 feet from second base and needs to make the throw to first base. Assuming the field is square, how far does she need to throw the ball? Round your answer to the nearest tenth. 90 feet distance. __ Feet.
13. Apply the Pythagorean Theorem to find the length between the two points. Round your answer to the nearest hundredth. 6, 9 and 2, 1.
14. Apply the Pythagorean Theorem to find the length between (2,7) and (-2,0). Round your answer to the nearest hundredth, if necessary.
A. 5.74
B. 11
C. 65
D. 8.06
15. Find the slant height of the square pyramid. Round to the nearest whole inch, if necessary. 12 in and 18 in.
A. 13 in
B. 6 in
C. 8 in
D. 15 in
16. Suppose a spider was able to create one thread that would extend from the top-right back corner of its tank to the bottom-left front corner. Approximately how long would that thread need to be for the tank below? The path of the spider's thread is shown with a red dotted line. Round your answer to the nearest tenth of an inch. the tank is 35 inches in length 16 inches tall and 12 inches wide.
The diagonal of the bottom of the tank is ___ inches. To the nearest tenth of an inch, the length of the spider's thread is ___ inches.
Answers are:
2. 80
3. 35 degrees
4. 22 degrees
5. 69
6. top is true false is bottom
7. 70
8. 29 in, 20 in, 21 in is right triangle and so is 63 in, 16 in, 65 in, the rest is not.
9. is not
10. 15
11. 8.9
12. 19.4 ft
13. 93.4 feet
14. 8.94
15. 8.06
16. 15 in
17. bottom of the tank is 37 and the spiders thread is 40.3
i got a bad grade but i hope the rest of u dont
1. To find the missing angle in a triangle, we can subtract the sum of the given angles from 180 degrees. In this case, the missing angle can be found by subtracting 15 degrees and 85 degrees from 180 degrees:
Missing angle = 180 degrees - 15 degrees - 85 degrees = 80 degrees
2. In a right triangle, the sum of the angles is always 180 degrees. Since one angle is already given as 55 degrees, we can find the measure of the third angle by subtracting the sum of the given angles from 180 degrees:
Third angle = 180 degrees - 90 degrees - 55 degrees = 35 degrees
3. The sum of the angles in a triangle is always 180 degrees. Thus, we can find angle x by subtracting 90 degrees and 112 degrees from 180 degrees:
Angle x = 180 degrees - 90 degrees - 112 degrees = -22 degrees
Since the result is negative, it is not possible for angle x to be negative in a triangle. Therefore, angle x does not have a valid measure in this case.
4. The sum of the angles in a triangle is always 180 degrees. Since two angles are already given as 37 degrees and 32 degrees, we can find the measure of the exterior angle (x) by subtracting the sum of the given angles from 180 degrees:
x = 180 degrees - 37 degrees - 32 degrees = 111 degrees
5. ∠6 = ∠5 is a true statement since both angles have a measure of 28 degrees.
6. Since lines P and Q are parallel, angle 8 and angle 2 are corresponding angles, which means they are congruent. Therefore, angle 2 also measures 110 degrees.
7. You have provided three sets of measurements for the lengths of sides. To determine if they can be the sides of a right triangle, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
For the first set of measurements (29 in, 20 in, 21 in), we have:
Hypotenuse = 29 in
Other two sides = 20 in and 21 in
Since 29^2 = 20^2 + 21^2 is not true, these measurements cannot describe the lengths of the sides of a right triangle.
For the second set of measurements (4 m, 5 m, 6 m), we have:
Hypotenuse = 6 m
Other two sides = 4 m and 5 m
Since 6^2 = 4^2 + 5^2 is true, these measurements can describe the lengths of the sides of a right triangle.
For the third set of measurements (63 in, 16 in, 65 in), we have:
Hypotenuse = 65 in
Other two sides = 63 in and 16 in
Since 65^2 = 63^2 + 16^2 is true, these measurements can describe the lengths of the sides of a right triangle.
8. To determine if the triangle is a right triangle, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
For the given triangle (6 cm, 3 cm, 4 cm), we have:
Hypotenuse = 6 cm
Other two sides = 3 cm and 4 cm
Since 6^2 = 3^2 + 4^2 is true, the triangle is a right triangle.
9. In a right triangle, the length of the hypotenuse can be found using 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 a right triangle with side lengths of 9 and 12, the length of the hypotenuse can be found as follows:
Hypotenuse^2 = 9^2 + 12^2 = 81 + 144 = 225
Hypotenuse = √225 = 15
Therefore, the length of the hypotenuse is 15.
10. In a right triangle, the lengths of the sides are related by 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 a right triangle with a leg measuring 8 inches and a hypotenuse measuring 12 inches, the length of the other leg can be found as follows:
Other leg^2 = 12^2 - 8^2 = 144 - 64 = 80
Other leg = √80 ≈ 8.9 inches
Therefore, the length of the other leg is approximately 8.9 inches.
11. To find the height above the ground reached by the top of the ladder, we 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 the given scenario, with the bottom of the ladder 5 feet from the base of the house, we have a right triangle formed by the ladder, the height, and the distance from the base of the house to the top of the ladder. Using the Pythagorean theorem, we can find the height as follows:
Height^2 = 20^2 - 5^2 = 400 - 25 = 375
Height = √375 ≈ 19.4 feet
Therefore, the top of the ladder touches the house at a height of approximately 19.4 feet.
12. Since the field is square, the distance she needs to throw the ball can be found by using 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 the given scenario, with the shortstop standing 25 feet from second base and needing to make the throw to first base, we have a right triangle formed by the throw distance, the distance from second base to the shortstop, and the distance from the shortstop to first base. Using the Pythagorean theorem, we can find the throw distance as follows:
Throw distance^2 = 25^2 + 90^2 = 625 + 8100 = 8725
Throw distance = √8725 ≈ 93.4 feet
Therefore, the shortstop needs to throw the ball approximately 93.4 feet.
13. To find the length between two points, we can use the distance formula. The distance formula states that the length between two points (x1, y1) and (x2, y2) is equal to the square root of [(x2 - x1)^2 + (y2 - y1)^2].
For the given points (6, 9) and (2, 1), the length between them can be found as follows:
Length = √[(2 - 6)^2 + (1 - 9)^2] = √[(-4)^2 + (-8)^2] = √[16 + 64] = √80 ≈ 8.94
Therefore, the length between the two points is approximately 8.94.
14. To find the length between two points, we can use the distance formula. The distance formula states that the length between two points (x1, y1) and (x2, y2) is equal to the square root of [(x2 - x1)^2 + (y2 - y1)^2].
For the given points (2, 7) and (-2, 0), the length between them can be found as follows:
Length = √[(-2 - 2)^2 + (0 - 7)^2] = √[(-4)^2 + (-7)^2] = √[16 + 49] = √65 ≈ 8.06
Therefore, the length between the two points is approximately 8.06.
15. To find the slant height of a square pyramid, we 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 the given square pyramid with a base side length of 12 inches and a height of 18 inches, we have a right triangle formed by half the diagonal of the base, the slant height, and the height of the pyramid. Using the Pythagorean theorem, we can find the slant height as follows:
Slant height^2 = (12/2)^2 + 18^2 = 36 + 324 = 360
Slant height = √360 ≈ 18.97 inches
Therefore, the slant height of the square pyramid is approximately 18.97 inches.
16. To find the length of the diagonal of the bottom of the tank, we 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 the given tank with dimensions 35 inches in length, 16 inches in height, and 12 inches in width, we have a right triangle formed by the length, height, and width of the tank. Using the Pythagorean theorem, we can find the length of the diagonal of the bottom of the tank as follows:
Diagonal length^2 = 35^2 + 16^2 + 12^2 = 1225 + 256 + 144 = 1625
Diagonal length = √1625 ≈ 40.31 inches
Therefore, the length of the diagonal of the bottom of the tank is approximately 40.31 inches. The length of the spider's thread would also be approximately 40.31 inches.