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Honors Algebra 2

Honors Algebra 2. Solving Right Triangle Problems. Answers to 6 Trig. Functions. Assignment Quiz.

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Honors Algebra 2

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  1. Honors Algebra 2 Solving Right Triangle Problems

  2. Answers to 6 Trig. Functions

  3. Assignment Quiz The lengths of the sides of a right triangle are 5 cm, 12 cm, and 13 cm. Sketch the triangle. Let theta represent the angle that is opposite the side whose length is 5 cm. Evaluate the six trigonometric functions of theta.

  4. Objective By the end of the lesson you should be able to use right triangle trigonometry to correctly arrive at a solution given a context.

  5. To solve right triangle problems: Always draw a diagram Label what you know Label what you need to find with a variable Choose a trig function based on what you know and what you need to find. Then it’s a piece of

  6. River Width To measure the river width you put a stake in the ground directly across from a boulder and walk 100 meters to the right. You then measure a 79 degree angle between the stake and boulder. What is the river width? boulder 79° 100m 514m

  7. Example: You are flying a kite 4 feet above the ground using 300 feet of line. With a wind speed of 40 miles per hour, the angle the kite line makes with the ground is . How high is the kite?

  8. When an object is above or below another object, you can find distances indirectly by using the angle of elevation or the angle of depression between the objects.

  9. Example 4: Geology Application A biologist whose eye level is 6 ft above the ground measures the angle of elevation to the top of a tree to be 38.7°. If the biologist is standing 180 ft from the tree’s base, what is the height of the tree to the nearest foot? Step 1 Draw and label a diagram to represent the information given in the problem.

  10. Example 4 Continued Step 2 Let x represent the height of the tree compared with the biologist’s eye level. Determine the value of x. Use the tangent function. Substitute 38.7 for θ, x for opp., and 180 for adj. 180(tan 38.7°) = x Multiply both sides by 180. 144 ≈ x Use a calculator to solve for x.

  11. Example 4 Continued Step 3 Determine the overall height of the tree. x + 6 = 144 + 6 = 150 The height of the tree is about 150 ft.

  12. 60.7° 120 ft You Try A surveyor whose eye level is 6 ft above the ground measures the angle of elevation to the top of the highest hill on a roller coaster to be 60.7°. If the surveyor is standing 120 ft from the hill’s base, what is the height of the hill to the nearest foot? Step 1 Draw and label a diagram to represent the information given in the problem.

  13. You Try Continued Step 2 Let x represent the height of the hill compared with the surveyor’s eye level. Determine the value of x. Use the tangent function. Substitute 60.7 for θ, x for opp., and 120 for adj. 120(tan 60.7°) = x Multiply both sides by 120. 214 ≈ x Use a calculator to solve for x.

  14. You Try Continued Step 3 Determine the overall height of the roller coaster hill. x + 6 = 214 + 6 = 220 The height of the hill is about 220 ft.

  15. Assignment Section 13.1 #20-22,23,42,45, 48-50 p 772-773

  16. Assignment Section 13.1 #20-22,23,42,45, 48-50 p 772-773

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