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4. 4 Applications A 1. 0 m long is placed against a building. The angle between the ladder and the ground is 61°. How high will the top of the ladder reach up the building? 0 m 61Њ Figure for 1 2. Construction An 18 ft ladder is leaning against a house. It touches the bottom of a window that is 14 ft 6 in. above the ground. What is the measure of the angle that the ladder forms with the ground? 3. Surveying When the angle of elevation of the sun is 58°, the shadow cast by a tree is 28 ft long. How tall is the tree?
Round your answer to the nearest mile. 68. Apparent Diameter The planet Uranus is 1,780 million miles from the sun and the sun has a diameter of 864,000 miles. To an observer on Uranus, what is the apparent diameter of the sun? Express your answer in decimal degrees to three decimal places. 72. Apparent Diameter Cordelia, another of Uranus’s moons, is 31,000 miles from Uranus. 03°. What is the diameter of Cordelia? Round your answer to the nearest mile. 2 Similar Triangles • Euclid’s Theorem and Similar Triangles • Applications Properties of similar triangles, stated in Euclid’s theorem that follows, are central to this section and form a cornerstone for the development of trigonometry.
Show that (sin u)2 + (cos u)2 = 1, using the deﬁnition of the trigonometric ratios (page 23) and the Pythagorean theorem. 48. In the ﬁgure that follows, side a was found two ways: one using a and sine, and the other using b and cosine. The graphing calculator screen shows the two calculations, but there is an error. Explain the error and correct it. 8 cm 60. Without looking back in the text, show that for each acute angle u: 1 (A) csc u = (B) cos(90° - u) = sin u sin u 61. Without looking back in the text, show that for each acute angle u: 1 (A) cot u = (B) csc(90° - u) = sec u tan u 62.