How long should an escalator be if it is to make an angle of 39° with the floor and carry people a vertical distance of 21 feet between floors? (Round your answer to the nearest whole number.)
Ratios
A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.
Trigonometric Ratios
Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.
Q: 1 How long should an escalator be if it is to make an
Q 2:Find AB if BC = 4, BD = 5, and AD = 2.
Q 3: This problem refers to right
Begin the problem by drawing a picture of the triangle with both the given and asked for information labeled appropriately.
If
find a. (Round your answer to three decimal places.)
Q:4 This problem refers to right triangle ABC with
Begin the problem by drawing a picture of the triangle with both the given and asked for information labeled appropriately.
If
find B. (Round your answer to two decimal places.)
Q:5 Using your calculator and rounding your answers to the nearest hundredth, find the remaining trigonometric ratios of θ based on the given information.
| cos θ | = | |
| sin θ | = | |
| tan θ | = | |
| cot θ | = | |
| csc θ | = |
Q:6 Use your calculator to find sin θ and cos θ if the point (9.38, 7.04) is on the terminal side of θ. (Round your answers to four decimal places.)
| sin θ | = | |
| cos θ | = |
Q:7 If a 78.0-foot flagpole casts a shadow 55.0 feet long, what is the angle of elevation of the sun (to the nearest tenth of a degree)?
Q:8Town L is 25 miles due south of town N. Town B is due east of town L and S 63° E from town N. How far is town L from town B? (Round your answer to the nearest whole number.)
Q:9he following problem involves directions in the form of bearing, which we defined in this section. Remember that bearing is always measured from a north-south line.
A boat leaves the harbor entrance and travels 26 miles in the direction N 41° E. The captain then turns the boat 90° and travels another 19 miles in the direction S 49° E. At that time, how far is the boat from the harbor entrance, and what is the bearing of the boat from the harbor entrance (see the figure below)? (Round your answers to the nearest whole number.)
| distance | mi | |
| bearing |
Q: 10 The following problem involves directions in the form of bearing, which we defined in this section. Remember that bearing is always measured from a north-south line.
A man wandering in the desert walks 2.7 miles in the direction S 35° W. He then turns 90° and walks 3.5 miles in the direction N 55° W. At that time, how far is he from his starting point, and what is his bearing from his starting point? (Round your answers to the nearest whole number.)
| distance | mi | |
| bearing |
Q:11 A man standing on the roof of a building 61.0 feet high looks down to the building next door. He finds the angle of depression to the roof of that building from the roof of his building to be 34.4°, while the angle of depression from the roof of his building to the bottom of the building next door is 63.7°. How tall is the building next door? (Round your answer to the nearest tenth.)
Q:12 An ecologist wishes to find the height of a redwood tree that is on the other side of a creek, as shown in the figure below. From point A he finds that the angle of elevation to the top of the tree is 9.4°. He then walks 24.8 feet at a right angle from point A to point B. There he finds that the angle between AB and a line extending from B to the tree is 85.7°. What is the height h of the tree? (Round your answer to one decimal place.)
h = ft
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