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Pythagorean Theorem and Trig Ratio Practice & Application Problems

1

5 pts

Find the missing side of the right triangle using the Pythagorean Theorem. Round to the nearest tenth if necessary.

2

10 pts

Kate's kite got stuck on the top branch of a tree. Kate is 15 feet from the base of the tree, and she knows that her kite string is 25 feet long. Draw Kate, her kite, and the tree below. Then use the Pythagorean Theorem to find what the height of the tree is, if the base of the tree and the ground form a right angle. Round to the nearest foot if needed.

3

3 pts

Looking at the information provided, choose the correct trigonometric ratio to find x in the following right triangle.

sine

cosine

tangent

4

10 pts

Cole wants to find out what the height of the street lamp at the end of his driveway. He notices that the shadow of the lamp in the morning is 12 feet long. If he stands at the tip of the shadow and looks up at the top of the lamp, his line of sight makes a 40 degree angle. Draw the right triangle formed by the street lamp, the shadow, and Cole's line of sight to the top of the lamp. Then use the correct trig ratio to find the height of the lamp.

5

7 pts

Solve for x using the correct trig ratio. (Hint: Inverse trig function!)

6

10 pts

Kate's mom watched Kate dealing with her kite in the earlier problem. She thought it was cute so she took a picture. Looking at the picture, she decides to find the angle of elevation from where Kate is holding the kite string to the top of the tree. Kate is still 15 feet from the base of the tree and the kite string is 25 feet long. Using that information, choose the correct trig ratio to find the angle of elevation from where Kate is holding the kite string to the top of the tree. Find the angle of elevation to the nearest degree.

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