Activity 3: Right Triangle Please!Direction: Write the formula that could be used to find theunknown part of the triangle in each item. DO NOT SOLVETHE UNKNOWN.y1. If X = 76° and x = 13 , findy.2. If X = 49° and x = 10 , find z.3. If x = 21.2 and X = 71°, find y.4. If x = 13 and Y = 16°, find z.5. If X = 19° and x = 11, find z.

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Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter3: Additional Topics In Trigonometry

Section3.1: Law Of Sines

Problem 47E: Environmental Science The bearing from the Pine Knob fire tower to the Colt Station fire tower is N...

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Albert lives in New Orleans. At noon on a summer day, the angle of elevation of the sun is 84. The window in Alberts room is 4.0 feet high and 6.5 feet wide. (Sec Figure 24.) a. Calculate the area of the floor surface in Alberts room that is illuminated by the sun when the angle of elevation of the sun is 84. b. One winter day the angle of elevation of the sun outside Alberts window is 37. Will the illuminated area of the floor in Alberts room be greater on the summer day, or on the winter day? Figure 24
The Learning Tower of Pisa The bell tower of the cathedral in Pisa, Italy, leans 5.6 from the vertical. A tourist stands 105 m from its base, with the tower leaning directly toward her. She measures the angle of elevation to the top of the tower to be 29.2. Find the length of the tower to the nearest meter.
Solve the right triangle shown at the right for all unknown sides and angles.
Airplane Ascent During takeoff, an airplane’s angle of ascent is 18 and its speed is 260 feet per second. (a) Find the plane’s altitude after 1 minute. (b) How long will it take for the plane to climb to an altitude of 10,000 feet?
Height of a Kite Valerie is standing directly below a kite. She observes that her own shadow is 4 feet long and the shadow of the kite lies 100 feet in front of her (see Figure 25). If Valerie is 6 feet tall, how high is the kite? Figure 25
Empire State Building You are standing 45 meters from the base of the Empire State Building. You estimate that the angle of elevation to the top of the 86th floor (the observatory) is 82. The total height of the building is another 123 meters above the 86th floor. What is the approximate height of the building? One of your friends is on the 86th floor. What is the distance between you and your friend?
Bridge Design A bridge is built across a small lake from a gazebo to a dock (see figure). The bearing from the gazebo to the dock is S 41 W. From a tree 100 meters from the gazebo, the bearings to the gazebo and the dock are S 74 E and S 28 E, respectively. Find the distance from the gazebo to the dock.
Laying Phone Cable City A lies on the north bank of a river that is 1 mile wide. You need to run a phone cable from City A to City B, which lies on the opposite bank 5 miles down the river. You will lay L miles of the cable along the north shore of the river, and from the end of that stretch of cable you will lay W miles of cable running under water directly toward City B. See Figure 2.108. Figure 2.108 You will need the following fact about right triangles: A right triangle has two legs, which meet at the right angle, and the hypotenuse, which is the longest side. An ancient and beautiful formula, the Pythagorean theorem, relates the lengths of the three sides: Lengthofhypotenuse=Lengthofoneleg2+Lengthofotherleg2 a. Find an appropriate right triangle that shows that W=1+(5L)2 b. Find a formula for the length of the total phone cable P from City A to City B as a function of L. c. Make a graph of the total phone cable length P as a function of L, and explain what the graph is showing. d. What value of L gives the least length for the total phone cable? Draw a picture showing the least-length total phone cable.

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