Exam 12: Introduction to Trigonometry

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The slant height of a regular square pyramid meets the apothem of the base to form an angle measuring 59°. If the length of the slant height is 12.6 cm, find the length of each side of the square base of the pyramid. Provide the answer correct to the nearest tenth of a centimeter.

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In the figure, m In the figure, m   = 90 ° and m   = 27 ° . Find the length of b correct to nearest tenth of a unit. = 90 ° and m In the figure, m   = 90 ° and m   = 27 ° . Find the length of b correct to nearest tenth of a unit. = 27 ° . Find the length of b correct to nearest tenth of a unit.

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Find the exact value of sin 30°.

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Across the flat terrain, Meg and Mara see a forest ranger tower that they know is 120 feet high. If their angle of elevation to the top of the tower is 3 degrees, how far (to the nearest foot)will Meg and Mara have to walk to get to the tower? [Hint: 1 mile = 5280 feet.]

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In the isosceles triangle shown, m In the isosceles triangle shown, m   = 30 ° while AC = AB = 10 inches. Find the area of the triangle. = 30 ° while AC = AB = 10 inches. Find the area of the triangle.

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In the 3-4-5 right triangle, find m In the 3-4-5 right triangle, find m   to the nearest degree. to the nearest degree.

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In In   , AB = 12, AD = 18, and m   = 56 ° . To the nearest square unit, find the area of   . , AB = 12, AD = 18, and m In   , AB = 12, AD = 18, and m   = 56 ° . To the nearest square unit, find the area of   . = 56 ° . To the nearest square unit, find the area of In   , AB = 12, AD = 18, and m   = 56 ° . To the nearest square unit, find the area of   . .

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In In   (not shown), m   = 90 ° . If a = 8, b = 15, and c = 17, find m   correct to the nearest degree. (not shown), m In   (not shown), m   = 90 ° . If a = 8, b = 15, and c = 17, find m   correct to the nearest degree. = 90 ° . If a = 8, b = 15, and c = 17, find m In   (not shown), m   = 90 ° . If a = 8, b = 15, and c = 17, find m   correct to the nearest degree. correct to the nearest degree.

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In a right triangle, In a right triangle,   . Find the value of   . . Find the value of In a right triangle,   . Find the value of   . .

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From a distance of 345 feet across a flat meadow, the top of a tower is seen through an angle of elevation of 27°. To the nearest foot, how tall is the tower?

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In a right triangle, the tangent ratio of an angle has the form In a right triangle, the tangent ratio of an angle has the form   . .

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In a right triangle, the measures of the angles are In a right triangle, the measures of the angles are   ,   , and   = 90 ° . With the lengths of the opposite sides being a , b , and c respectively, find tan   . , In a right triangle, the measures of the angles are   ,   , and   = 90 ° . With the lengths of the opposite sides being a , b , and c respectively, find tan   . , and In a right triangle, the measures of the angles are   ,   , and   = 90 ° . With the lengths of the opposite sides being a , b , and c respectively, find tan   . = 90 ° . With the lengths of the opposite sides being a , b , and c respectively, find tan In a right triangle, the measures of the angles are   ,   , and   = 90 ° . With the lengths of the opposite sides being a , b , and c respectively, find tan   . .

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In In   ,   is a right angle while SR = 11 and ST = 13. To the nearest degree, what is the measure of   ? , In   ,   is a right angle while SR = 11 and ST = 13. To the nearest degree, what is the measure of   ? is a right angle while SR = 11 and ST = 13. To the nearest degree, what is the measure of In   ,   is a right angle while SR = 11 and ST = 13. To the nearest degree, what is the measure of   ? ?

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In In   , the lengths of the sides are a = 8, b = 10, and c = 12. To the nearest degree, find m   . , the lengths of the sides are a = 8, b = 10, and c = 12. To the nearest degree, find m In   , the lengths of the sides are a = 8, b = 10, and c = 12. To the nearest degree, find m   . .

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Find the exact value of tan 60°.

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If m If m   = 67 ° , b = 17.4 cm, and c = 12.5 cm, find the area of   correct to the nearest square centimeter. = 67 ° , b = 17.4 cm, and c = 12.5 cm, find the area of If m   = 67 ° , b = 17.4 cm, and c = 12.5 cm, find the area of   correct to the nearest square centimeter. correct to the nearest square centimeter.

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Given that cos Given that cos   = 0.5, it follows that = 0.5, it follows that

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  is not a right triangle. If m   = 72 ° , m   = 38 ° , AB = 12.4, and BC = 19.2, find the length of   correct to the nearest whole unit.[Hint: Consider altitude   .] is not a right triangle. If m   is not a right triangle. If m   = 72 ° , m   = 38 ° , AB = 12.4, and BC = 19.2, find the length of   correct to the nearest whole unit.[Hint: Consider altitude   .] = 72 ° , m   is not a right triangle. If m   = 72 ° , m   = 38 ° , AB = 12.4, and BC = 19.2, find the length of   correct to the nearest whole unit.[Hint: Consider altitude   .] = 38 ° , AB = 12.4, and BC = 19.2, find the length of   is not a right triangle. If m   = 72 ° , m   = 38 ° , AB = 12.4, and BC = 19.2, find the length of   correct to the nearest whole unit.[Hint: Consider altitude   .] correct to the nearest whole unit.[Hint: Consider altitude   is not a right triangle. If m   = 72 ° , m   = 38 ° , AB = 12.4, and BC = 19.2, find the length of   correct to the nearest whole unit.[Hint: Consider altitude   .] .]

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In a right triangle, the cosine ratio takes the form In a right triangle, the cosine ratio takes the form   . .

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The lengths of the sides of a right triangle are a , b , and c (the hypotenuse). Given that The lengths of the sides of a right triangle are a , b , and c (the hypotenuse). Given that   , find an expression for   . , find an expression for The lengths of the sides of a right triangle are a , b , and c (the hypotenuse). Given that   , find an expression for   . .

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