# Right triangle + Pythagorean theorem - problems

1. The pond
We can see the pond at an angle 65°37'. Its end points are 155 m and 177 m away from the observer. What is the width of the pond?
2. Sphere from tree points
Equation of sphere with three point (a,0,0), (0, a,0), (0,0, a) and center lies on plane x+y+z=a
3. A truck
A truck departs from a distribution center. From there, it goes 20m west, 30m north and 10m west and reaches a shop. How can the truck reach back to the distribution center from the shop (what is the shortest path)?
4. Find the 5
Find the equation with center at (1,20) which touches the line 8x+5y-19=0
5. Two people
Two straight lines cross at right angles. Two people start simultaneously at the point of intersection. John walking at the rate of 4 kph in one road, Jenelyn walking at the rate of 8 kph in the other road. How long will it take for them to be 20√5 km apar
6. Right triangle from axes
A line segment has its ends on the coordinate axes and forms with them a triangle of area equal to 36 sq. Units . The segment passes through the point ( 5,2). What is the slope of the line segment. ?
7. Cone 15
The radius of the base of a right circular cone is 14 inches and it's height 18 inches. What is the slant height?
8. Garden
Area of square garden is 6/4 of triangle garden with sides 56 m, 35 m and 35 m. How many meters of fencing need to fence a square garden?
9. Trapezoid MO
The rectangular trapezoid ABCD with right angle at point B, |AC| = 12, |CD| = 8, diagonals are perpendicular to each other. Calculate the perimeter and area of ​​the trapezoid.
10. Right Δ
Right triangle has length of one leg 51 cm and length of the hypotenuse 85 cm. Calculate the height of the triangle.
11. Axial section
Axial section of the cone is equilateral triangle with area 208 dm2. Calculate volume of the cone.
12. Circle chord
What is the length d of the chord circle of diameter 36 m, if distance from the center circle is 16 m?
13. Trigonometric functions
In right triangle is: ? Determine the value of s and c: ? ?
14. Rectangle
The rectangle is 11 cm long and 45 cm wide. Determine the radius of the circle circumscribing rectangle.
15. Cuboid
Cuboid with edge a=24 cm and body diagonal u=50 cm has volume V=17280 cm3. Calculate the length of the other edges.
16. Tetrahedral pyramid
What is the surface of a regular tetrahedral (four-sided) pyramid if the base edge a=10 and height v=18?
17. Triangle SAS
Calculate area and perimeter of the triangle, if the two sides are 51 cm and 110 cm long and angle them clamped is 130°.
18. Movement
From the crossing of two perpendicular roads started two cyclists (each at different road). One runs at average speed 24 km/h, the second at average speed 16 km/h. Determine the distance between them after 35 minutes cycling.
19. Square
Points A[-9,6] and B[-5,-3] are adjacent vertices of the square ABCD. Calculate area of the square ABCD.
20. Is right?
Is triangle with sides 51, 56 and 77 right triangle?

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