Optimization with angles. A drainage canal is constructed so its cross section isshaped like a trapezoid with equally sloping sides. If the bottom and sides each have length 5 feet, what angle θ would yield the greatest cross-sectional area?

Q: an airplane is flying from New Orleans to Atlanta. As the airplane is about to finish its course,…

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Q: A mason wants to be sure she has a right corner in a building’s foundation. She marks a point 3 ft…

A: Given,           A mason wants to be sure she has a right corner in a building’s foundation. She…

Q: If we have a triangle which has one of its side c = 2 and angles A = π/4 and B = π/3. Workout the…

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Q: diagram

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Q: A surveyor wishes to determine the width of a pond. From a point A at one end of the pond, he marks…

A: According to the given problem BC is the width of the pond .

Q: The students in a science club planted a rectangular flower garden in front of their school. The…

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Q: The figure shows a region to be covered with plywood under a set of stairs. The area of that region…

A: Area of the triangle is given as follows Where a and b are the sides C is the angle A is the area

Q: A balloonist is directly above a straight road 1.7 miles long that joins two towns. She finds that…

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Q: An irrigation channel is constructed by bending a sheet of metal that is 3 m wide, as shown in the…

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Q: What are the basics to Geometry ?

A: Geometry is the mathematics involving points, lines, curves. Hence, the basics of geometry starts…

Q: DATE: NO. 1. Find the lengths of the sides of triangle ABC and state whether the triangle is a right…

A: Step 1: Step 2: Step 3: Step 4:

Q: Adjacent sides of a parallelogram are 11 cm and 17 cm. If the length of one of its diagonals is 26…

A: We know, in a parallelogram, p2+q2 = 2a2+b2 where, p and q are the lengths of the diagonals. a and b…

Q: A landscape designer is working on the plans for a residential yard. Her client wants a privacy…

A: We have to find the number of hedge plants required.

Q: Two hikers are at opposite sides of a mountain, ready to begin their hike. The height of the…

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Q: How can we apply the Pythagorean theorem to the reference right triangle?

A: The Pythagorean theorem states that the if the length of the two sides of the triangle are known,…

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.