The length of the hypotenuse of a 30° 60° and 90° triangle is 11 what is the perimeter
In a 30° 60° 90° triangle, the length of the hypotenuse is twice the shorter leg. So the shorter leg is 11/2. The longer leg (opposite the 60° angle) is √3 times the shorter leg, so it is 11/2 x √3.
The perimeter is the sum of all three sides, so:
Perimeter = 11/2 + 11/2 x √3 + 11
Perimeter = 11/2(1+√3) + 11
Perimeter = 5.5(1+√3) + 11
Perimeter ≈ 29.95
So the perimeter is approximately 29.95 units.
What is the missing value to the nearest hundredth
Tan__=7
A.54.94
B.56.94
C.81.87
D.85.94
Without knowing the angle, we cannot determine the missing value for the tangent function. However, we can use a calculator to find the angle whose tangent is 7, to the nearest hundredth.
Using the inverse tangent function (tan^-1) on a calculator:
tan^-1(7) ≈ 81.87 degrees
Therefore, the missing value to the nearest hundredth is 81.87 degrees, which corresponds to option C.
Find the area of a trapezoid
10 cm, 5 cm,3cm With 45 degree angle
To find the area of a trapezoid with bases b1 and b2 and height h, we use the formula:
Area = (b1 + b2) / 2 * h
In this case, we are not given which side of the trapezoid is the longer base (b1) or the shorter base (b2). However, we do know that the trapezoid has a 45 degree angle and the sides adjacent to this angle are 5 cm and 3 cm.
We can use the trigonometric ratio for the tangent of 45 degrees (tan(45) = opposite/adjacent = 1) to find the height of the trapezoid.
tan(45) = h / 5 (opposite is the height, adjacent is 5)
h = 5
Now we can use the formula for the area of a trapezoid, using b1 as the longer base and b2 as the shorter base:
Area = (b1 + b2) / 2 * h
Since we do not have the measured length of the third side, we cannot determine the bases. Therefore, the answer cannot be calculated with the given information.
To find the perimeter of the triangle, we need to know the lengths of all three sides. In a 30°-60°-90° triangle, the side opposite the 30° angle is half the length of the hypotenuse, and the side opposite the 60° angle is (√3)/2 times the length of the hypotenuse.
Given that the length of the hypotenuse is 11, we can calculate the lengths of the other two sides as follows:
Side opposite the 30° angle = (1/2) * 11 = 5.5
Side opposite the 60° angle = (√3/2) * 11 = 9.527
Now, to find the perimeter, we add up the lengths of all three sides:
Perimeter = 5.5 + 9.527 + 11
Perimeter ≈ 25.027
Therefore, the perimeter of the triangle is approximately 25.027 units.
To find the perimeter of the triangle, we need to know the lengths of all three sides. In a 30°-60°-90° triangle, the side opposite the 30° angle is half the length of the hypotenuse, and the side opposite the 60° angle is (√3 / 2) times the length of the hypotenuse.
Given that the hypotenuse is 11, we can find the lengths of the other sides as follows:
Length of the side opposite the 30° angle = (1/2) * 11 = 5.5
Length of the side opposite the 60° angle = (√3 / 2) * 11
To find the value of (√3 / 2) * 11, we can evaluate it using a calculator or the square root (√) and division (/) functions.
Calculating (√3 / 2):
- The square root of 3 (√3) is approximately 1.732.
- Divide 1.732 by 2 to get 0.866.
Multiplying 0.866 by 11 gives us 9.526.
Therefore, the length of the side opposite the 60° angle is approximately 9.526.
Now, we can find the perimeter by adding the lengths of all three sides:
Perimeter = 5.5 + 9.526 + 11
Perimeter = 26.026
Therefore, the perimeter of the triangle is approximately 26.026 units.