2 EXAMPLE 3Standardized Test PracticeSOLUTIONThe flagpole and the woman form sides of two right triangles with the ground, as shown below. The sun’s rays hit the flagpole and the woman at the same angle. You have two pairs of congruent angles, so the triangles are similar by the AA Similarity Postulate.
3 Standardized Test Practice EXAMPLE 3Standardized Test PracticeYou can use a proportion to find the height x. Write 5 feet 4 inches as 64 inches so that you can form two ratios of feet to inches.x ft64 in.50 ft40 in.=Write proportion of side lengths.40x = 64(50)Cross Products Propertyx = 80Solve for x.The flagpole is 80 feet tall. The correct answer is C.ANSWER
4 GUIDED PRACTICEfor Example 34.What If ? A child who is 58 inches tall is standing next to the woman in Example 3. How long is the child’s shadow?58 in.x8050 ft.
5 You can use a proportion to find the length of the shadow (x). GUIDED PRACTICEfor Example 3SOLUTIONThe flagpole and the child next to the women form sides of two right triangles with the ground, here, there are two pairs of congruent angles, so the triangles are similar by the AA similarity postulate.You can use a proportion to find the length of the shadow (x).58x=8050Write proportion of side length80x =Cross product propertyx = 36.25Solve for x
6 GUIDED PRACTICEfor Example 3The length of the shadow is in. long.ANSWER
7 GUIDED PRACTICEfor Example 35.You are standing in your backyard, and you measure the lengths of the shadows cast by both you and a tree. Write a proportion showing how you could find the height of the tree.SOLUTIONTree heightYour height=Length of your shadowLength of shadow