The bases of a trapezoid are 25 and 15 respectively. The angles at the extremities of one base are 65 degree and 35 degree respectively find the two legs. pls help me, thank you!
In trapezoid ABCD, let the altitude from C be CE and the altitude from D be DF. That is, FECD is a rectangle, with base FE.
Now collapse the trapezoid to eliminate the rectangle. Then CD=0 and AB=10 and you have a triangle with
angle C = 180-65-35 = 80°
10/sin80° = AD/sin35° = BC/sin65°
To find the lengths of the two legs of the trapezoid, we can use the Law of Sines.
Let's denote the length of the longer leg as 'a' and the length of the shorter leg as 'b'.
We know that the angles at the extremities of one base are 65 degrees and 35 degrees, so we can write:
sin(65°) = a / 25
sin(35°) = b / 15
To find the lengths of 'a' and 'b', we need to solve these two equations simultaneously.
Let's first solve for 'a' by rearranging the first equation:
a = 25 * sin(65°)
a ≈ 25 * 0.9063
a ≈ 22.66 (rounded to two decimal places)
Now, let's solve for 'b' by rearranging the second equation:
b = 15 * sin(35°)
b ≈ 15 * 0.5736
b ≈ 8.61 (rounded to two decimal places)
Therefore, the lengths of the two legs of the trapezoid are approximately 22.66 and 8.61.
To find the lengths of the legs of a trapezoid, we will use the properties of the angles and the given information.
Let's label the trapezoid as ABCD, where AB and CD are the parallel bases of length 25 and 15 respectively. The angles at the extremities of base AB are given as 65 degrees and 35 degrees.
Step 1: Draw a diagram
Draw a trapezoid ABCD with base AB as the bottom base. Label the angles as given (65 degrees and 35 degrees).
Step 2: Find the third angle
The sum of the angles in any quadrilateral is 360 degrees. In trapezoid ABCD, we have three angles (65 degrees, 35 degrees, and the third angle). Therefore, we can find the third angle by subtracting the sum of the two given angles from 360 degrees.
Third angle = 360 degrees - 65 degrees - 35 degrees
Step 3: Find the fourth angle
Since opposite angles in a trapezoid are equal, the fourth angle is equal to the third angle.
Step 4: Use the angles to find the heights
Draw a line segment from the top vertex of the trapezoid (vertex C) perpendicular to base AB. This line segment represents the height of the trapezoid.
Use trigonometric ratios (sine, cosine, tangent) to find the length of the height. The height can be found by using the length of one leg and the corresponding angle.
Step 5: Calculate the lengths of the legs
Now that we know the height (perpendicular distance from base AB to base CD), we can use the properties of the trapezoid to find the lengths of the legs.
The lengths of the legs of a trapezoid can be calculated using the formula:
Leg Length = (Height / (tan(Angle1) + tan(Angle2)))
Substitute the values of the height and the angles into the formula to find the lengths of the legs. In this case, the height is found in step 4, and the angles are given as 65 degrees and 35 degrees.
Leg Length1 = (Height / (tan(65 degrees) + tan(35 degrees)))
Leg Length2 = (Height / (tan(65 degrees) + tan(35 degrees)))
Using these steps, you can calculate the lengths of the legs of the trapezoid.