Citizenship by Lucia Raatma

By Lucia Raatma

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4173 in the column labeled sin A at the top. 2 Find cos 72Њ. 3090 in the column labeled cos A at the bottom. 4460. Read up the page since 55Њ20Ј > 45Њ. 1171. Read down the page since 41Њ50Ј < 45Њ If the number of minutes in the given angle is not a multiple of 10, as in 24Њ43Ј, interpolate between the values of the functions of the two nearest angles (24Њ40Ј and 24Њ50Ј) using the method of proportional parts. 4 Find sin 24Њ43Ј. 0008 when rounded off to four decimal places. 4181. 5 Find cos 64Њ26Ј.

What is the angle the diagonal makes with the longer side? Ans. 30 377 m A tower 45 m high casts a shadow of 12 m. What is the angle of elevation of the sun? Ans. 4 ft A parked car is spotted from a hotel window which is 100 m above the car. 4Њ, how far is the car from the window? Ans. 8Њ with the horizontal. How far must the train go up the track for it to gain 30 m in altitude? Ans. 1 Bearing The bearing of a point B from a point A in a horizontal plane is usually defined as the angle (always acute) made by the ray drawn from A through B with the north-south line through A.

In the right triangle ABC: (a) Side a < side c; therefore sin A ϭ a/c < 1. (b) Sin A ϭ cos A when a/c ϭ b/c; then a ϭ b, A ϭ B, and A ϭ 45Њ. (c) Sin A < 1 (above) and csc A ϭ 1/sin A > 1. (d) Sin A ϭ a/c, tan A ϭ a/b, and b < c; therefore a/c < a/b or sin A < tan A. (e) Sin A < cos A when a < b; then A < B or A < 90Њ Ϫ A and A < 45Њ. (f) Tan A ϭ a/b > 1 when a > b; then A > B and A > 45Њ. 8 Find the exact values of the trigonometric functions of 45Њ. (See Fig. ) Fig. 12 In any isosceles right triangle ABC, A ϭ B ϭ 45Њ and a ϭ b.

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