How long should an escalator be if it is to make an angle of 33 degree with the

Question

How long should an escalator be if it is to make an angle of 33 degree with the floor and carry people a vertical distance of 21 ft between floors? A road up a hill makes an angle of 5.1 degree with the horizontal. If the road from the bottom of the hill to the top of the hill is 2.5 mi long, how high is the hill? A 72.5-ft rope from the top of circus tent pole is anchored to the ground 43.2 ft from the bottom of the pole. What angle does the rope make with the pole? (Assume the pole is perpendicular to the ground.) A ladder is leaning against the top of a 7.0-ft wall. If the bottom of the ladder is 4.5 ft from the wall, what is the angle between the ladder and the wall? If a 73.0-ft flagpole casts a shadow 51.0 ft long, what is the angle of elevation of the sun (to the nearest tenth of a degree)? If the angle of elevation of the sun is.63.4 degree when a building casts a shadow of 37.5 ft, what is the height of the building? A person standing 150 cm from a mirror notices that the angle of depression from his eyes to the bottom of the mirror is 12 degree, while the angle of elevation to the top of the minor is 11 degree. Find the vertical dimension of the mirror. (See Figure 14.) A person standing on top of a 15-ft high sand pile wishes to estimate the width of the pile. He visually locates two rocks on the ground below at the base of the sand pile. The rocks are on opposite sides of the sand pile, and he and the two rocks are in line with one another. If the angles of depression from the top of the sand pile to each of the rocks are 27 degree and 19 degree, how far apart are the rocks? Figure 15 shows the topographic map we used in Example 4 of this section. Recall that Stacey is at position S and Amy is at position A. In Figure 15, Travis, a third hiker, is at position T. If the distance between A and T on the map in Figure 15 is 0.5 inch, find each of the following: the horizontal distance between Amy and Travis the difference in elevation between Amy and Travis the angle of elevation from Travis to Amy If the distance betweens S and T on the map in Figure 15 is 5/8 inch, find each of the following: the horizontal distance between Stacey and Travis the difference in elevation between Stacey and Travis the angle of elevation from Travis to Stacey A boat leaves the harbor entrance and travels 25 mi in the direction N 42 degree E. The captain then turns the boat 90 degree and travels another 18 mi in the direction S 48 degree At that time how far is the boat from the harbor entrance, and what is

Explanation / Answer

5) length of elevlator is the hypotensue of right angled triangle = x

height = vertical distance from floor = 21 ft

slope = 33 deg

So, sin33 = 21/x

x = 21/sin33 = 38.55 ft

6) slope = 5.1 deg

hypoetenuse = length of road = 2.5 mi

Let height of hill be x

So, sin5.1 = x/2.5

x = 0.22 miles is the height if hill

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