Roberto has plans to build a tree house in a large oak tree in his backyard. He takes measurements from the ground and uses trigonometry to estimate how tall the tree house can be. Twenty feet from the base of the tree, Roberto measures a 26.6° angle of elevation to the proposed bottom of the tree house and a 42° angle of elevation to the proposed top of the tree house. If Roberto is 6 ft tall, will there be enough room for him to stand inside the tree house?

Q: from a hot air balloon 2 km high, a person look east sees one town with angle of depression of 12…

A:

Q: Two apartment buildings are 40 ft apart. From a window in her apartment, Izzi can see the top of the…

A: Given that the distance between two apartment buildings are 40 ft. apart. The diagram according to…

Q: The plans for a concrete patio call for a 6 ft by 7 ft slab of concrete 6 inches thick, which has a…

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Q: A 15 feet support wire is attached to a telephone pole at a point 9.5 feet below the top of the pole…

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Q: How high does a 17-foot-tall temporary support post reach when it is positioned at a 30° angle to…

A: Let height be h and we know that in a right angle triangle  sinθ=side opposite to…

Q: Fred was measuring the height of a building. He stood standing at some distance from the building…

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Q: A six foot man is standing 80 feet away from a building.  He looks up at a 30° angle to see the top…

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Q: A carpenter constructs a table with four legs that each forms an acute angle with the tabletop. Each…

A: Solve by using pythogorous theorem.

Q: A 6-foot-tall worker stands 40 feet away from a crumbling tower. The angle of elevation to the top…

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Q: A surveyor observes that the angle between the road and the bottom of a bridge girder is 30 degrees.…

A: Given data is : Angle θ=30∘ Bridge clearance is 16.5 feet. To find the horizontal distance from the…

Q: Gabe can see the top of the fountain by looking up at an angle of 39o . If Gabe is 1.3m tall and the…

A: Given that Gabe can see the top of the fountain at an angle of 39 degree. If Gabe is 1.3 m tall and…

Q: From Point S, Samantha uses a clinometer to determine the angle of elevation to the top of the cliff…

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Q: Kara is standing on the edge of a 15-foot high diving board. Her friend, Sierra, is treading water…

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Q: An architect is designing a two-story house that is located at 40°N latitude. The architect wants to…

A: How much roof overhang should the architect provide so that at noon on the day of the summer…

Q: The Statuary Hall in the United States Capitol is elliptical. It measures 46 ft wide and 96 ft long.…

A: Here I am attaching image so that you understand each and every step.

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.