Warm Up 8 5 Solve the triangle above. Angles of Elevation and Depression - Applications of our trig functions! Application #1 A 35 foot ladder is leaned up against the side of a house at a 65ْ angle with the ground. Find the distance from the base of the house to the foot of the ladder and the height reached by the ladder. Surveyors #2: A surveyor sighted from the bank of a river directly across it to a tree on the opposite bank. He then turned exactly 90° to the right, and paced off 200 feet. He then sighted the same tree with an angle of 20°. How wide is the river? r = 72.79 ft Vocabulary • Angle of elevation • Angle of depression Drawing and accurately labeling a diagram is essential in problem solving!!!!!! 1. From a point on the ground 150 meters from the base of a cliff, the angle of elevation to the top is 27 degrees. How high is the cliff? 2. An airplane climbed 1250 feet while making 3 miles of airline distance (horizontal distance). Find the angle at which the airplane climbed. Note: 1 mile = 5280 feet 3. From a lighthouse which stands 40 meters above the level of a lake, the angle of depression of a buoy on the water is 18 degrees. Find the distance of the buoy from the base of the lighthouse. Now a bit harder: 4. From the window of an office building, the angle of elevation of the top of the Empire State Building is 57 degrees and the angle of depression of a point on the ground directly below the top of the skyscraper is 13 degrees. The buildings are known to be 167 feet apart. How high is the Empire State Building? 57 13 Not to scale......at all. Two Step Problems CN tower in Toronto Canada • The angle of elevation to the top of the building is 43° and the angle of elevation to the top of the antenna is 61°. If the glass floor is 342 m tall, what is the height of the “sky pod”? Warm Up • Two office buildings are 29 ft apart. The height of the taller building is 609 ft. The angle of depression from the top of the taller building to the top of the shorter building is 15°. Find the height of the shorter building. 5. A vertical tree stands on a slope that is inclined at an angle of 12 degrees with the horizontal. When the angle of the sun measures 30 degree, the shadow of the tree down the slope is 18 meters long. How tall is the tree? Challenge: From the top of a 30 meter high lighthouse, the keeper measures the angles of depression to two boats, one directly west of the lighthouse and the Second due south. The angles of depression are found to be 8 and 14 degrees, Respectively. How far are the two boats apart? (to the nearest tenth) • A meteorologist measures the angle of elevation of a weather balloon as 41°. A radio signal from the balloon indicates that it is 1503 m from her location. How high is the weather balloon above the ground? • The world’s tallest unsupported flagpole is 282 ft tall in Surrey, British Colombia. The shortest shadow cast by the pole during the year is 137 ft long. What is the angle of elevation of the sun when the shortest shadow is cast?