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SOLVING A RIGHT TRIANGLE GIVEN TWO SIDES

10/4/13 Warm Up . SOLVING A RIGHT TRIANGLE GIVEN TWO SIDES. Solve right triangle ABC , if a = 29.43 cm and c = 53.58 cm. Trig Game Plan Date: 10/4/13. Angles of Elevation or Depression.

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SOLVING A RIGHT TRIANGLE GIVEN TWO SIDES

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  1. 10/4/13 Warm Up SOLVING A RIGHT TRIANGLE GIVEN TWO SIDES Solve right triangle ABC, if a = 29.43 cm and c = 53.58 cm.

  2. Trig Game Plan Date: 10/4/13

  3. Angles of Elevation or Depression The angle of elevation from point X to point Y (above X) is the acute angle formed by ray XY and a horizontal ray with endpoint X. The angle of depression from point X to point Y (below X) is the acute angle formed by ray XY and a horizontal ray with endpoint X.

  4. Caution Be careful when interpreting the angle of depression. Both the angle of elevation and the angle of depression are measured between the line of sight and a horizontal line.

  5. Solving an Applied Trigonometry Problem Step 1 Draw a sketch, and label it with the given information. Label the quantity to be found with a variable. Step 2 Use the sketch to write an equation relating the given quantities to the variable. Step 3 Solve the equation, and check that your answer makes sense.

  6. Example 3a: I DO IT, SO WATCH! FINDING THE ANGLE OF ELEVATION WHEN LENGTHS ARE KNOWN The length of the shadow of a building 34.09 m tall is 37.62 m. Find the angle of elevation of the sun. tan The angle of elevation is about 42.18°.

  7. Example 3b: WE DO IT TOGETHER! FINDING THE ANGLE OF ELEVATION WHEN LENGTHS ARE KNOWN The length of a shadow of a flagpole 55.20 ft tall is 27.65 ft. Find the angle of elevation of the sun. Four significant digits The angle of elevation of the sun is 63.39°.

  8. Example 3c: YOU DO IT! 22.02 m B 28.34 m FINDING THE ANGLE OF ELEVATION WHEN LENGTHS ARE KNOWN The length of the shadow of a tree 22.02 m tall is 28.34 m. Find the angle of elevation of the sun. Draw a sketch. The angle of elevation of the sun is 37.85.

  9. Example 4 FINDING A LENGTH WHEN THE ANGLE OF ELEVATION IS KNOWN When Shelly stands 123 ft from the base of a flagpole, the angle of elevation to the top of the flagpole is 26°40′. If her eyes are 5.30 ft above the ground, find the height of the flagpole. Since Shelly’s eyes are 5.30 ft above the ground, the height of the flagpole is 61.8 + 5.30 = 67.1 ft

  10. Example 5 The measure of equals the measure of the angle of depression because the two angles are alternate interior angles, so Finding a Length When the Angle of Elevation is Known The angle of depression from the top of a tree to a point on the ground 15.5 m from the base of the tree is 60.4°. Find the height of the tree.

  11. Example 5 Finding a Length When the Angle of Elevation is Known Three significant digits The tree is about 27.3 m tall.

  12. A plane if flying at an elevation of 27000 feet. It is within sight of the airport and the pilot finds that the angle of depression to the airport is 25 degrees. Find the distance between the plane and the airport.

  13. A plane if flying at an elevation of 27000 feet. It is within sight of the airport and the pilot finds that the angle of depression to the airport is 25 degrees. Find the distance between the plane and the airport. angle of elevation = 25° distance from plane to airport 27000 feet airport distance from a point on the ground directly below the plane to the airport

  14. angle of elevation = 25° 65° distance from plane to airport 27000 feet airport distance from a point on the ground directly below the plane to the airport A plane if flying at an elevation of 27000 feet. It is within sight of the airport and the pilot finds that the angle of depression to the airport is 25˚. Find the distance between the plane and the airport. The distance from the plane to the airport is 64,000 feet

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