1529.3 square unit is the area of the cheetah area at a zoo is designed in a triangular fashion, surrounded on all three sides by sidewalks, given that the property has 67 feet of frontage on one sidewalk, and 48 feet of frontage on another; these two sidewalks intersect at a 72° angle. This can obtained by using the formula of Area of a Triangle with 2 Sides and Included Angle.
<h3>Find the area of the cheetah area at the zoo:</h3>
Area of a triangle is obtained using the formula of Area of a Triangle with 2 Sides and Included Angle.
If in a triangle ΔABC,
- 1/2 × bc × sin(A), if b and c are two sides of a triangle and angle A is the included angle
- 1/2 × ac × sin(B), if a and c are two sides of a triangle and angle B is the included angle
- 1/2 × ab × sin(C), if a and b are two sides of a triangle and angle C is the included angle
Here it is given that,
67 feet and 48 feet are the sides of the triangular space and angle 72° is the included angle.
By using the formula of Area of a Triangle with 2 Sides and Included Angle,
Area of the cheetah area = 1/2 × bc × sin(A)
Area of the cheetah area = 1/2 × (67)(48) × sin(72°)
sin(72°) = 0.951056516
Area of the cheetah area = 1608 × 0.951056516
Area of the cheetah area = 1529.29888 ≈ 1529.3 square unit
Hence 1529.3 square unit is the area of the cheetah area at a zoo is designed in a triangular fashion, surrounded on all three sides by sidewalks, given that the property has 67 feet of frontage on one sidewalk, and 48 feet of frontage on another; these two sidewalks intersect at a 72° angle.
Learn more about area of triangle here:
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