-- How to solve right triangles Trigonometry -- How to solve right triangles

Agenda Attention Vocabulary Sum of the Angles in a Triangle Pythagorean Theorem Tangent Sine Cosine Applying the Trigonometric Ratios

Hypotenuse Legs Right Angle

Attention Trigonometry only happens in right triangle. The ratio of any two sides remains constant even if the triangle is enlarged or reduced. (Similar triangles) B3 26 cm B2 29 cm 35 cm B1 25 cm 37 cm 14 cm A C3 C2 C1

Vocabulary  

Angle of inclination：the acute angle between the horizontal and a line or line segment Angle of elevation: the angle between the horizontal through eye level and a line of sight to a point above eye level Angle of depression: the angle between the horizontal through eye level and a line of sight to a point below eye level Indirect measurement: a measurement made using a ratio, formula, or other mathematical reasoning Angle of depression Angle of inclination Angle of elevation

Sum of the Angles in a Triangle In any triangle, the sum of the measures of the three angles is always equal to 180º B 100° 42° 38° A C

Pythagorean Theorem In any right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides (legs). A   c b B C a

Example   10 cm 6 cm X

Tangent(tan)   A c Adjacent b B C a Opposite

Example 1 Determine the Tangent Rations for Angles   X 12 Y Z 6

Example 2 Using the Tangent Ratio to Determine the Measure of Angle   H 5 4 G J

Example 3 Using the Tangent to Determine an Angle of Inclination The latitude of Fort Smith, NWT, is approximately 60 °. Determine whether this design for a solar panel is the best for Fort Smith. Justify your answer. A Solar panel 9ft C 12ft B

Solution   Solar panel A 9ft C 12ft B

Sine(sin) and Cosine(cos)   hypotenuse A c Adjacent b C B a Opposite

Example 1 Determine the Sine and Cosine of an Angle   E 12cm 5cm D F 13cm

Example 2 Using the Tangent Ratio to Determine the Measure of Angle   8 K M 3 N

Example 3 Using Sine or Cosine to Solve a Problem A water bomber is flying at an altitude of 5000ft. The plane’s radar shows that it is 8000ft from the target site. What is the angle of elevation of the plane measured from the target site, to the nearest degree? A 8000ft 5000ft X R

Solution   A 8000ft 5000ft R X

Applying 3A ladder is 6.5m long. It leans against a wall. The base of the ladder is 1.2m from the wall. What is the angle of inclination of the ladder to the nearest tenth of a degree?

From the top of a 20-m high building , a surveyor measured the angle of elevation of the top of another building and the angle of depression of the base of that building. The surveyor sketched this plan of her measurements. Determine the height of the taller building to the nearest tenth of a meter.

More Nowadays we are learning the function,let us see the consine function and the sine function. 2018/6/9