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Check it out! 1 2.2.3: Problem Solving with the Pythagorean Theorem and Trigonometry

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2 Chris is mounting a shelf on a wall to hold his awards. He is attaching the shelves using mounting brackets that are shaped like right triangles. He wants the width of each shelf to fit the length of the bracket perfectly, as shown in the diagram. If the width of the shelves is 21 inches, will the shelves fit the length of the bracket exactly?

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1.Draw the right triangle represented and assign a variable to the length of the bracket. 2.Use trigonometry to calculate the length of the bracket. Round to the nearest tenth of an inch. 3.Will the shelves fit exactly? Why or why not? 3 2.2.3: Problem Solving with the Pythagorean Theorem and Trigonometry

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1.Draw the right triangle represented and assign a variable to the length of the bracket. 4 2.2.3: Problem Solving with the Pythagorean Theorem and Trigonometry

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2.Use trigonometry to calculate the length of the bracket. Round to the nearest tenth of an inch. s is the side opposite the given angle, and the hypotenuse is given. Use sine to calculate the length of the bracket. The length of the bracket, s, is about 20.5 inches. 5 2.2.3: Problem Solving with the Pythagorean Theorem and Trigonometry

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3.Will the shelves fit exactly? Why or why not? The shelves have a width of 21 inches but the brackets have a length of about 20.5 inches. The shelves will not fit exactly; they will be slightly wider. 6 2.2.3: Problem Solving with the Pythagorean Theorem and Trigonometry

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