4) The length of one diagonal of a rhombus is 12 cm. The measure of the angle opposite that diagonal is 60º. What is the perimeter of the rhombus?
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1 Name Date Period MM2G1. Students will identify and use special right triangles. MM2G1a. Determine the lengths of sides of triangles. MM2G1b. Determine the lengths of sides of triangles. 1) The area of a square is 10 square centimeters. What is the product of the lengths of the diagonals of the square? 2) A parallelogram has sides that are 10 cm and 20 cm long. The measure of the acute angles of the parallelogram is 30. What is the area of the parallelogram? 3) What is the area of a regular hexagon with sides that are 10 cm long? 4) The length of one diagonal of a rhombus is 12 cm. The measure of the angle opposite that diagonal is 60º. What is the perimeter of the rhombus? 1
2 5) Quadrilateral LMTP is an isosceles trapezoid. What is the length of LP? 6) A rhombus is show below. If the height, h, intersects the base at its midpoint, what is the height of the rhombus? 7) A right triangle is shown below. What is the approximate value of h? 8) What is the closest value of t for the triangle with the dimension shown below? 2
3 MM2G2. Students will define and apply sine, cosine, and tangent ratios to right triangles. MM2G2a. Discover the relationship of the trigonometric ratios for similar triangles. MM2G2b. Explain the relationship between the trigonometric ratios of complementary angles. 9) Angle J and angle K are complementary angles in a right triangle. The value of tan J is. What is the value of sin J? Triangle RST is a right triangle with right angle S, as shown. What is the area of triangle RST? 10) is an altitude of, and. The measure of is, and. What is the approximate length of? From a point 12 feet from the base of a building, the angle of elevation from the ground to the top of the building is. What is the height of the building? 3
4 MM2G2. Students will define and apply sine, cosine, and tangent ratios to right triangles. MM2G2c. Solve application problems using the trigonometric ratios. A road ascends a hill at an angle of 15. For every 100 feet of road, how many feet does the road ascend? According to building codes, the maximum angle of ascent for a staircase in a home is To get from the first floor to the second floor in a new home, a staircase will have a total vertical distance of inches. What is the minimum horizontal distance, to the nearest inch, needed for the staircase? 4
5 Bianca uses an angle-measuring device on a 3-foot tripod to find the height, h, of a weather balloon above ground level, as shown in this diagram. The balloon is at a 40 angle of elevation. A radio signal from the balloon tells Bianca that the distance between the tripod and the balloon is 25,000 feet. Write an expression to represent the height, h, of the balloon above ground level? 11) Use this diagram of a cone to answer the question. The base of the cone has a radius of 6 cm. Which expression represents the slant height, in centimeters, of the cone? What is the volume of the cone? (remember: V = 1/3 bh) 5
6 12) A dead tree was struck by lightning, causing it to fall over at a point 10 up from its base. If the fallen treetop forms a angle with the ground, about how tall was the tree originally? 13) A ladder is leaning against the side of a building. The ladder is 30 feet long, and the angle between the ladder and the building is. About how far is the foot of the ladder from the building? 14) The angle of elevation from point G on the ground to the top of a flagpole is. The height of the flagpole is 60 feet. Write the equation to find the distance from point G to the base of the flagpole. 15) The diagram below shows the side view of a house. The base of its roof is 4 meters above ground level. Point P is the highest point on the roof. Based on the diagram, what is the distance from P to the ground level? 6
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