A triangular flower garden has a an area of 28 m2. Two of its edges are 14 metres and 8 metres. Find the angle between the two edges.
Area of triangle = (1/2)(side1)(side2)sinθ , where θ is the
angle between them
28 = (1/2)(14)(8)sinθ
sinθ = .5
θ = 30°
1/2(14*8)sin c [28] =(1/2x14x8 sin c) 28÷56=0.5 sun 0.5=30°
To find the angle between the two edges of the triangular flower garden, you can use the law of cosines. The law of cosines states that for a triangle with sides lengths a, b, and c, and angle C opposite the side c, the following equation applies:
c^2 = a^2 + b^2 - 2ab * cos(C)
Given that the two edges of the triangular flower garden are 14 m and 8 m, we can label them as follows:
a = 14 m (longer edge)
b = 8 m (shorter edge)
Since the area of the triangular garden is given as 28 m^2, we can use the formula for the area of a triangle to calculate the height of the triangle:
Area = (1/2) * base * height
28 m^2 = (1/2) * 8 m * height
height = 7 m
Now, we can calculate the length of the third side using the Pythagorean theorem, since the height divides the triangle into two right-angled triangles:
c^2 = a^2 + height^2
c^2 = 14^2 + 7^2
c^2 = 196 + 49
c^2 = 245
c ≈ 15.65 m
Now, we can plug the values into the law of cosines equation to find the angle C:
15.65^2 = 14^2 + 8^2 - 2(14)(8) * cos(C)
243.9225 = 196 + 64 - 224 * cos(C)
243.9225 = 260 - 224 * cos(C)
-16.0775 = -224 * cos(C)
cos(C) ≈ -16.0775 / -224
cos(C) ≈ 0.0719
Using the inverse cosine function (cos^(-1)), we can find the angle C:
C ≈ cos^(-1)(0.0719)
C ≈ 84.75 degrees
Therefore, the angle between the two edges of the triangular flower garden is approximately 84.75 degrees.
To find the angle between two edges of a triangular flower garden, we can use the Law of Cosines.
The Law of Cosines states that in a triangle with sides a, b, and c, and angle C opposite side c, the following equation holds:
c^2 = a^2 + b^2 - 2ab * cos(C)
In this case, we have two sides, 14 meters and 8 meters, so we'll label them as a and b respectively. The angle between these two sides will be C.
First, we need to find the length of the third side, c, using the formula for the area of a triangle:
Area = (1/2) * base * height
Since the triangle is equilateral, we can use either a or b as the base and solve for the height:
28 = (1/2) * 8 * height
Simplifying, we get:
56 = 8 * height
height = 56 / 8 = 7 meters
Now, let's calculate the length of side c using the Pythagorean theorem:
c^2 = a^2 + height^2
c^2 = 14^2 + 7^2
c^2 = 196 + 49
c^2 = 245
c = sqrt(245) = 15.65 meters (approximately)
Now, we can use the Law of Cosines to find the angle C:
c^2 = a^2 + b^2 - 2ab * cos(C)
(15.65)^2 = 14^2 + 8^2 - 2 * 14 * 8 * cos(C)
245 = 196 + 64 - 224 * cos(C)
245 = 260 - 224 * cos(C)
224 * cos(C) = 15
cos(C) = 15 / 224
C = arccos(15 / 224)
Using a calculator or a table of cosines, we find that the approximate value of C is 79.92 degrees. Therefore, the angle between the two edges is approximately 79.92 degrees.