An isosceles triangle has a base 22 cm long and a base angle of 72 degrees. Find its perimeter.
construct the right angled triangle, let the hypotenuse be h
cos 72 = 11/h
h = 11/cos72 = ....
perimeter = 22 + 2h = ....
The 2 unequal side if a parallelogram measure 4.8 inches and 8.3 inches, respectively. If the longer diagonal measure is 11.2 inches, find the lenght of the shorter diagonal.
To find the perimeter of an isosceles triangle, we need to know the length of its equal sides.
Since the base angle is 72 degrees, we know that the other two angles are also 72 degrees each. In an isosceles triangle, the base angles are equal.
Let's call the length of each equal side "x."
To find "x," we can use the trigonometric property of isosceles triangles:
cos(angle) = adjacent side / hypotenuse
In our case, we can use cosine since we know the angle and the adjacent side (half the base, which is 22 cm/2 = 11 cm).
cos(72 degrees) = 11 cm / x
To find "x," we can rearrange the equation:
x = 11 cm / cos(72 degrees)
Using a calculator, we find:
x ≈ 11 cm / 0.309 = 35.59 cm
The length of each equal side is approximately 35.59 cm.
To find the perimeter, we add the lengths of all three sides:
Perimeter = base + equal side + equal side
= 22 cm + 35.59 cm + 35.59 cm
= 93.18 cm
Therefore, the perimeter of the isosceles triangle is approximately 93.18 cm.
To find the perimeter of an isosceles triangle, we need to know the lengths of all three sides.
In this case, we are given that the triangle has a base length of 22 cm. Since it's an isosceles triangle, the other two sides are equal in length.
To find the length of the equal sides, we can use the angles of the triangle. Since the base angle is given as 72 degrees, we can use trigonometric functions to find the lengths.
Let's call the length of the equal sides "x". Using the trigonometric identity for an isosceles triangle, we can write:
2x * sin(72 degrees/2) = 22 cm
Simplifying this equation, we get:
2x * sin(36 degrees) = 22 cm
Now, we can solve for x by dividing both sides of the equation by 2 * sin(36 degrees):
x = 22 cm / (2 * sin(36 degrees))
Using a calculator to find sin(36 degrees) ≈ 0.5878, we get:
x ≈ 22 cm / (2 * 0.5878) ≈ 18.75 cm
So, the length of each equal side is approximately 18.75 cm.
Now that we know the lengths of all three sides, we can find the perimeter by summing the lengths:
Perimeter = base + 2 * equal sides
Perimeter = 22 cm + 2 * 18.75 cm
Perimeter ≈ 22 cm + 37.5 cm ≈ 59.5 cm
Therefore, the perimeter of the isosceles triangle is approximately 59.5 cm.