Solving Right Triangles

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Presentation transcript:

Solving Right Triangles OBJECTIVES: Solve a right triangle Use right triangles to solve real-life problems

Background Every right triangle has one right angle, two acute angles, one hypotenuse and two legs. Solve a right triangle: determine the measurements of all angles and sides of a right triangle You can solve a right triangle if you know either of the following: Two side lengths One side length and one acute angle measure

Two Side lengths Solve the right triangle Begin by using the Pythagorean Theorem to find the length of the missing side Then, find the measure of one of the acute angles using the inverse trig function keys on your calculator and the sides given based on the angle you want to solve for first in the problem Finally, find the other acute angle by using Complementary angles

EX 1: Solve the right triangle 1. Y 25 14 X y Z

One Side length and One Acute angle Solve the right triangle Begin by finding the missing angle using complementary angles Finally, use the trig functions to find the missing side lengths using the given angle and given side

EX 2: Solve the right triangle 2. C b A 19 c B

Applications Many practical applications of trigonometry in surveying, construction, aeronautics and other fields involve indirect measurement. Indirect measurement is a technique used to measure something when the use of measuring devices is either impractical or impossible. In order to see an object above the eye level, you must raise your line of sight by an acute angle Angle of elevation: the angle formed from the horizontal at your eye level to the raised or elevated line of sight Angle of depression: the angle from a horizontal at the top of the object to the line of sight below

EX 3: 3. You lean a 16 foot ladder against the wall. If the base is 4 feet from the wall, what angle does the ladder make with the ground?

EX 4: 4. You sight a rock climber on a cliff at an angle of elevation. You eye level is 6 feet above the ground and you are 1000 feet from the base of the cliff. What is the approximate height of the rock climber from the ground?

EX 5: 5. An airplane pilot sights a life raft at an angle of depression. The airplane’s altitude is 3 kilometers. What is the airplane’s horizontal distance from the raft?

Solving Right Triangles WS