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Name: ________________________________ TP: _______ CW#78: GRASP – Pythagorean, Special Right, Trig Geometry CRS CLASS OF 2015 AVERAGE MASTERY PPF602: Use the Pythagorean Theorem 51% PPF601: Apply properties of 30-60-90, 45-45-90, similar, and congruent triangles 48% FUN 502 Express sine, cosine, and tangent of an angle in a right triangle as a ratio of given side lengths 46% FUN602: Apply basic trigonometric ratios to solve righttriangle problems. 56% You will GGGGGRRRRRRRRRRRRRRRRRRRRRRRRAAAAAAAASSSSSSSSSSSSSSSSSSSSPPPPPP the following problems! They are application problems, which means they are MORE difficult. If you want to increase your mastery, these problems are the way to get there! 1) Pythagorean. In your town, there is a field that is in the shape of a right triangle. One leg is 35 feet, and the hypotenuse measures 80 feet. A) Find the perimeter of the field. B) You are going to plant dogwood seedlings about every ten feet around the field’s edge. How many trees do you need? C) If each dogwood seedling sells for $12, how much will the trees cost? 2) Pythagorean. In baseball, the distance of the paths between each pair of consecutive bases is 90 feet and the paths form right angles. How far does the ball need to travel if it is thrown from home plate directly to second base? PUSH IT TO THE LIMIT. 3) Special Right Triangles. The area of the shaded region is 45 inches squared. Find the missing hypotenuses for both triangles. 7√2 in. 4) Special Right Triangles. Each figure below is a 30°-60°-90° triangle. Find the value of x. Round to the nearest 5) Trigonometry. A person flying a kite has released 176 m of string. The string makes an angle of 27° with the ground. How high is the kite? How far away is the kite horizontally? Answer to the nearest meter. PUSH IT TO THE LIMIT. 6) Trigonometry. Find the perimeter of the larger triangle. Round intermediate values to the nearest tenth. Use the rounded values to calculate the next value. Round your final answer to the nearest tenth. 7) Trigonometry. Two vertical poles, one 3 meters tall and the other 5 meters tall, stand a certain distance apart. A line from the top of the shorter pole to the top of the taller pole makes a 15 angle with a horizontal line. Which of the following expresses the horizontal distance, in meters, between the bases of the two poles (rounded to the nearest hundredth)? PUSH IT TO THE LIMIT. 8) Trigonometry. From a stationary hot-air balloon 500 ft above the ground, two sightings of a lake are made (see figure). How long is the lake? 9) PUSH IT TO THE LIMIT. Name: ______________________________________ TP: _____ EXIT SLIP Score: ______ / 1 Pick one of the two problems for your exit slip. #1 is easier, and #2 is more of a challenge. Pick the appropriate level of difficulty for YOU! 1) A person flying a kite has released 176 m of string. The string makes an angle of 27° with the ground. How high is the kite? How far away is the kite horizontally? Answer to the nearest meter. 2) To measure the height of a building, two sightings are taken a distance of 50 ft apart. If the first angle of elevation is 40° and the second is 32°, what is the height of the building? h 32⁰ 50 ft. 40⁰ x PUSH IT TO THE LIMIT. PUSH IT TO THE LIMIT.