# Right triangle - math word problems

- One side

One side is 36 long with a 15° incline. What is the height at the end of that side? - Annular area

The square with side a = 1 is inscribed and circumscribed by circles. Find the annular area. - Lateral surface area

The ratio of the area of the base of the rotary cone to its lateral surface area is 3: 5. Calculate the surface and volume of the cone, if its height v = 4 cm. - Cincinnati

A map is placed on a coordinate grid. Cincinnati located at (5,4) and San Diego is located at (-10, -3). How far apart is Cincinnati from San Diego on the map? Round to the nearest tenth. - Two boats

Two boats are located from a height of 150m above the surface of the lake at depth angles of 57° and 39°. Find the distance of both boats if the sighting device and both ships are in a plane perpendicular to the surface of the lake. - A kite

ABCD is a kite. Angle OBC = 20° and angle OCD = 35°. O is the intersection of diagonals. Find angle ABC, angle ADC and angle BAD. - Area of a rectangle

Calculate the area of a rectangle with a diagonal of u = 12.5cm and a width of b = 3.5cm. Use the Pythagorean theorem. - The tractor

The tractor sows an average of 1.5 ha per hour. In how many hours does it sows a rectangular trapezoid field with the bases of 635m and 554m and a longer arm 207m? - The Eiffel Tower

The top of the Eiffel Tower is seen from a distance of 600 meters at an angle of 30 degrees. Find the tower height. - The ladder

The ladder has a length of 3 m and is leaning against the wall, and its inclination to the wall is 45°. How high does it reach? - The cable car

The cable car has a length of 3,5 kilometers and an angle of climb of 30 degrees. What is the altitude difference between Upper and Lower Station? - Company logo

The company logo consists of a blue circle with a radius of 4 cm, which is an inscribed white square. What is the area of the blue part of the logo? - Base of prism

The base of the perpendicular prism is a rectangular triangle whose legs length are at a 3: 4 ratio. The height of the prism is 2cm smaller than the larger base leg. Determine the volume of the prism if its surface is 468 cm^{2}. - Depth angles

At the top of the mountain stands a castle, which has a tower 30 meters high. We see the crossroad in the valley from the top of the tower and heel at depth angles of 32° 50 'and 30° 10'. How high is the top of the mountain above the crossroad - Chauncey

Chauncey is building a storage bench for his son’s playroom. The storage bench will fit into the corner and against two walls to form a triangle. Chanuncy wants to buy a triangular shaped cover for the bench. If the storage bench is 2 1/2 ft. Along one w - Touch x-axis

Find the equations of circles that pass through points A (-2; 4) and B (0; 2) and touch the x-axis.

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