Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Warm up: Pythagorean Theorem Review 1. What is it? 1. When do we use it? 1. Why is it important? Can we use the Pythagorean Theorem to find x? x 10 52° Trigonometry!!! • From Greek: • Trigo = Triangle • Metr = measure • So it means MEASURING TRIANGLES!! 38 Which SIDES is adjacent? Opposite? The hypotenuse? 52 leg B A leg C Hypotenuse = side opposite right angle Opposite side = the leg that’s farthest away and not touching the angle Adjacent side = the leg that is closest to the angle Trigonometric Ratio • A trigonometric ratio or a ratio of the lengths of two sides of a right triangle. • There are three basic trig ratios we will be looking at today: sine, cosine, and tangent. Trigonometry Ratios KEY CONCEPT: RATIO SINE TRIG RATIOS WORDS sin = opposite hypotenuse SYMBOLS MODELS Sin A = 4 5 5 A 4 3 COSINE cos = adjacent hypotenuse cosA = 3 5 5 4 A 3 TANGENT tan= opposite adjacent tanA= 4 3 5 4 A 3 Shortcut! • SOH CAH TOA is a suuuuper way to remember the trig ratios! Sin Opposite Hypotenuse Cos Adjacent Hypotenuse Tangent Opposite Adjacent Express each ratio as a fraction and as a decimal (hundredths place) a) sin A b) cos A c) tan A d) sin B e) cos B NOT ON WORKSHEET f) tan B On your own! a) sin A b) cos A c) tan A d) sin B e) cos B f) tan B Warm Up Use Pythagorean theorem to solve for the missing side then set up each ration a) sin A A b) cos A c) tan A d) sin B B e) cos B f) tan B C On your calculator: Press the sin, cos or tan button, enter the angle measure, close the parentheses and hit enter • sin30 = • cos45 = • tan78 = • cos50 = • tan37 = • sin50 = You must first make sure that your calculator is in degree mode PAY CLOSE ATTENTION!!! Finding a missing side using trig • Solve for the indicated side. Steps 1) 2) 3) 4) 5) Choose a reference angle Label the sides Choose the correct ratio Setup the equation Solve Find x 3 x 60° Find x. 30 ° x 5 On your own! x 32° 18 Here’s the tricky part: how can we do this backwards? 3 4 x° Use the inverse functions on your calculator! • SIN-1 • COS-1 • TAN-1 Find x (round to the ones place): 1)sinx= .75 2)cosx = .80 3)tanx = .54 x° Find x. Round to the nearest tenth. Solve for x. Round to the nearest tenth. On your own Do Now Today we’re learning some new terms: Angle of depression and Angle of Elevation. a.) What do you think angle of depression is? b.) What do you think angle of elevation is? TRIG IN THE REAL WORLD!! Trig can be used in real life! • To talk about trig in the real world, you need to know a few definitions: • ANGLE OF ELEVATION: The angle between the upward line of sight to an object and the horizon . angle of elevation • Tyrell went to the fair and saw a cute girl on the ferris wheel. He was like, “Oh snap! Shawty right there is a ten! I wonder how high up she is!” So he used his protractor (that he always carries with him) to find the angle of elevation and found that it was 47°. If he was standing 20 feet from the ferris wheel, what was its height? On your own: Brionna was out on Lake Gaston on a boat with her cousins and they saw a high cliff and thought it would be fun to jump off it into the water. but Brionna was like, “Wait, let’s figure out it’s height first.” So they found the angle of elevation to be 39°. And they measured that they were 50 ft from the cliff. Should they jump off? A roofer props a ladder against a wall so that the top of the ladder reaches a 30foot roof that needs repair. If the angle of elevation from the bottom of the ladder to the roof is 55°, how far is the ladder from the base of the wall? Round your answer to the nearest foot. ON YOUR OWN Suppose the sun casts a shadow off a 35-foot building. If the angle of elevation to the top of the building is 60°, how long is the shadow to the nearest tenth of a foot? angle of depression • ANGLE OF DEPRESSION: The angle between the downward line of sight to an object and the horizon. • The angle of depression is always congruent to the angle of elevation. angle of depression angle of depression ? 35° 50 ft angle of depression 22° ? 82 ft Kyle is at the end of a pier 30 feet above the ocean. His eye level is 3 feet above the pier. He is using binoculars to watch a whale surface. If the angle of depression of the whale is 20°, how far is the whale from Kyle’s binoculars? 1. The angle of elevation from the base to the top of a waterslide is about 28˚. The slide extends horizontally about 45.8 meters. Estimate the height h of the slide. 2. An 18-foot ladder is leaning against a wall. The foot of the ladder is 6 feet from the base of the wall. What is the approximate measure of the angle the ladder forms with the ground? 3. The control tower views a plane landing at a 19° angle of depression, as show. How far is the plane from the base of the control tower? 114 ft.