1. Right triangle has an angle that is 58deg…what is the measure of the 3rd angle?
2. A triangle has sides of 10, 9, 13 cm. Can it be a right triangle? Prove
3. Find the distance between points (-2,3) and (4,1). Round answer to nearest tenth.
4. Find the diagonal of a rectangular prism box that has measures of 3 x 4 x 10 cm. Round to nearest tenth.
5. A circus tent is the shape of a square pyramid. It has a base edge of 20meter, a slant height of 13.5m. Find the height of the tent. Round to nearest tenth.
1. The sum of the angles in a triangle is always 180 degrees. Since we know that one angle is 90 degrees (a right angle) and another angle is 58 degrees, we can find the measure of the third angle by subtracting the sum of the other two angles from 180 degrees.
Third angle = 180 degrees - 90 degrees - 58 degrees
Third angle = 180 degrees - 148 degrees
Third angle = 32 degrees
Therefore, the measure of the third angle in the right triangle is 32 degrees.
2. To determine if a 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 other two sides.
In this case, if the triangle has sides of 10, 9, and 13 cm, we can check if it satisfies the Pythagorean Theorem:
10^2 + 9^2 = 13^2
100 + 81 = 169
181 ≠ 169
Since the values do not satisfy the Pythagorean Theorem, the triangle with sides of 10, 9, and 13 cm is not a right triangle.
3. To find the distance between two points, we can use the distance formula:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
In this case, the points are (-2, 3) and (4, 1). Plugging the values into the distance formula:
Distance = √((4 - (-2))^2 + (1 - 3)^2)
Distance = √((4 + 2)^2 + (1 - 3)^2)
Distance = √((6)^2 + (-2)^2)
Distance = √(36 + 4)
Distance = √40
Distance ≈ 6.32
Therefore, the distance between the points (-2, 3) and (4, 1) is approximately 6.32 units.
4. The diagonal of a rectangular prism (or cuboid) can be found using the formula:
Diagonal = √(length^2 + width^2 + height^2)
In this case, the rectangular prism has dimensions 3 cm x 4 cm x 10 cm. Plugging the values into the formula:
Diagonal = √(3^2 + 4^2 + 10^2)
Diagonal = √(9 + 16 + 100)
Diagonal = √(125)
Diagonal ≈ 11.2
Therefore, the diagonal of the rectangular prism box measures approximately 11.2 cm.
5. To find the height of the 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 (the slant height in this case) is equal to the sum of the squares of the other two sides.
In this case, if the base edge of the pyramid is 20 meters and the slant height is 13.5 meters, we can find the height as follows:
Height^2 = (slant height)^2 - (base edge)^2/4
Height^2 = 13.5^2 - (20^2)/4
Height^2 = 182.25 - 100
Height^2 = 82.25
Height ≈ 9.08
Therefore, the height of the circus tent is approximately 9.1 meters.