An isosceles triangle has an area of 24 yd², and the angle between the two equal sides is 166°. Find the length of the two equal sides.
Let x = base of triangle
Let y = height of triangle
Area of triangle is (1/2) base times height, so
A = (1/2)xy
24 = (1/2)xy
48 = xy : eqn(1)
If the angle between the two equal sides is 166°, then the remaining angles are:
1/2(180° - 166°) = 7° each
In your drawing of triangle,
tan(angle) = opposite / adjacent
tan(7°) = height of triangle / 1/2 of base of triangle
tan(7°) = y / (1/2x) : eqn(2)
Now you have two equations, two unknowns.
From eqn(2), we can rewrite this as:
tan(7°) = y / (1/2 x)
y = 0.1228 (1/2 x)
y = 0.06138x
Substitute this to eqn(1):
48 = xy
48 = x(0.06138x)
48 = 0.06138x^2
x^2 = 48 / 0.06138
x^2 = 781.857
x = 27.96
Thus, the height is
48 = (27.96)y
y = 1.72
And the length of an equal side is (use Pythagorean Theorem):
(length of an equal side)^2 = (1/2 x)^2 + y^2
(length of an equal side)^2 = (0.5 * 27.96)^2 + 1.72^2
Continue solving for the length, units in yards. Hope this helps~ `u`
To find the length of the two equal sides of the isosceles triangle, we can start by using the formula for the area of a triangle.
The formula for the area of a triangle is:
Area = (1/2) * base * height
For an isosceles triangle, the two equal sides are the base and the height.
Let's assume that each equal side has a length of 'x' yards.
Since the triangle is isosceles, the base and height are both 'x' yards.
Now, let's substitute the values into the formula:
Area = (1/2) * base * height
24 = (1/2) * x * x
Simplifying the equation:
24 = (1/2) * x^2
Multiplying both sides of the equation by 2 to eliminate the fraction:
48 = x^2
Now, let's take the square root of both sides of the equation to find the value of 'x':
√48 = √x^2
x = √48
Simplifying the square root of 48:
x ≈ 6.93
Therefore, the length of the two equal sides of the isosceles triangle is approximately 6.93 yards.