Area of SAS & ASA Triangles quiz #1 Flashcards
Area of SAS & ASA Triangles quiz #1
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What is the general formula for the area of a triangle when two sides and the included angle are known (SAS case)? The area is given by (1/2) * a * b * sin(C), where a and b are the side lengths and C is the included angle. Which type of triangle's area can be calculated using the trigonometric area formula involving sine? Any triangle where two sides and the included angle (SAS) are known, or where two angles and a side (ASA) are known and the missing side can be found using the Law of Sines. What is the sum of the interior angles of a pentagon? The sum of the interior angles of a pentagon is 540 degrees. How do you find the area of a triangle when you know two sides and the included angle? Use the formula: Area = (1/2) * side1 * side2 * sin(included angle). For which triangles is it appropriate to use the trigonometric area formula involving sine? It is appropriate for triangles where two sides and the included angle (SAS) are known, or for ASA triangles after finding the missing side using the Law of Sines. What is the area of a circle with a radius of 1 foot? The area is π square feet. How do you find the area of a triangle when given two angles and the included side (ASA case)? First, use the Law of Sines to find a missing side, then use the area formula: Area = (1/2) * known side * found side * sin(included angle). What is the general formula for the area of a sector of a circle with radius r and central angle θ (in radians)? The area is (1/2) * r^2 * θ. How do you find the area of a sector of a circle given the radius and the central angle in radians? Use the formula: Area = (1/2) * r^2 * θ, where r is the radius and θ is the central angle in radians. How do you find the area of a sector of a circle given the radius and the central angle in radians? The area is (1/2) * r^2 * θ, where r is the radius and θ is the central angle in radians. How do you find the area of a rectangle that is 11 units long and 5 units wide? Multiply the length by the width: Area = 11 * 5 = 55 square units. Which formula can be used to calculate the area of a sector in a circle given the radius and central angle in radians? Area = (1/2) * r^2 * θ, where r is the radius and θ is the central angle in radians. How do you find the area of a regular octagon inscribed in a circle of radius r? Divide the octagon into 8 congruent isosceles triangles, find the area of one using (1/2) * r^2 * sin(π/4), and multiply by 8: Area = 4 * r^2 * sin(π/4). What is the area of a sector with a central angle of 90 degrees and a radius of 1 foot? The area is (1/4) * π square feet, since 90 degrees is 1/4 of a full circle. How do you find the area of a triangle with side lengths 30, 40, and 50? Use Heron's formula: s = (30 + 40 + 50)/2 = 60, then Area = sqrt[s(s-30)(s-40)(s-50)]. How many sides does a polygon have if the sum of the interior angles is 3420 degrees? Use the formula (n-2) * 180 = 3420. Solving for n gives n = 21. How many sides does a polygon have if the sum of the interior angles is 1440 degrees? Use the formula (n-2) * 180 = 1440. Solving for n gives n = 10. How do you find the area of the region that lies inside both curves r = 7 sin(θ) and r = 7 cos(θ)? Find the area common to both polar curves by integrating (1/2)[(7 sin(θ))^2] and (1/2)[(7 cos(θ))^2] over the region where they overlap, typically from θ = 0 to θ = π/2, and sum or subtract as appropriate.
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