Parts of a Right Triangle B Acute Angle

Parts of a Right Triangle B Acute Angle Leg e us en A ot yp H Right Angle Leg That was easy ber Remem e that th is nuse hypote the always de. t si longes C Acute Angle

Trigonometry of the Right Triangle There are three Trigonometric Ratios that we will be using. Sine Cosine Tangent sin cos tan In order to use three Trigonometric Ratios, you must understand the concept of adjacent sides and opposite sides when compared to a specific angle in a triangle. Let’s take a look at some examples.

Adjacent Side vs Opposite Side A When comparing to angle A Side a is the opposite side. Side b is the adjacent side. Side c is the hypotenuse. When comparing to angle B c b Side b is the opposite side. Side a is the adjacent side. Side c is the hypotenuse. C a B

Using the Trigonometric Functions A c b How am I supposed to remember that? C a B

Remembering the Trigonometric Functions SOH I P N P E O S I T E Y P O T E N U S E CAH O S I N E D J A C E N T Y P O T E N U S E TOA A N G E N T P P O S I T E D J A C E N T

Trigonometric Functions with Numbers A 5 4 That’s not so hard. I can do that. C 3 B

Applying the Trigonometric Functions The lengths of the sides of triangle ABC are given. For each triangle Find: a) Sin A b) Cos A c) Tan A A 16 C A 20 12 45 B C A 51 24 11 B C 5 B That was easy

Homework Page 357: 3 – 10 All Problems

Evaluating Trigonometric Functions Make sure your calculator is in degree mode.

Trigonometric Word Problems A 34 foot ladder leaning against a vertical wall reaches a height of 30 feet. Find the sine, cosine, and tangent values of the angle that the ladder makes with the ground. I should probably draw a picture. Remember the Pythagorean Theorem. A 34 B 16 30 C Asi De Facil

Another Trigonometric Word Problem The bed of a truck is 6 feet above the ground. The driver uses a ramp 10 feet long to load the truck. Find: a) the sine, cosine, and tangent of the angle that the ramp makes with the ground. b) The measurement of the angle that the ramp makes with the ground to the nearest degree. A 10 6 C 8 B It’s Sam Ting no matter which function I use. That was easy

Angle of Elevation From a point at sea 85 feet from a lighthouse, the tangent of the angle of elevation to the top of the lighthouse is. How tall is the lighthouse? Angle of elevation h A 85 Asi De Facil

Angle of Depression The angle of depression from the top of a lighthouse to a ship at point A is 37 o. If the ship is 110 feet away from the lighthouse, find to the nearest foot, the height of the lighthouse. Method 1 37 o Angle of depression 53 o h Method b 37 o 110 That was easy

Homework Page 357: 16 – 19 All Problems