# River

From the observatory 11 m high and 24 m from the river bank, river width appears in the visual angle φ = 13°. Calculate width of the river.

Result

y =  29.5 m

#### Solution:

$h = 11 \ m \ \\ x = 24 \ m \ \\ A = (13^\circ \rightarrow rad) = (13 \cdot \ \dfrac{ \pi }{ 180 } \ ) = 0.226892802759 \ \\ B = \arctan (x/h) = \arctan (24/11) \doteq 1.141 \ \\ C = A+B = 0.2269+1.141 \doteq 1.3679 \ rad \ \\ c = 180/\pi \cdot \ C = 180/3.1416 \cdot \ 1.3679 \doteq 78.3764 \ ^\circ \ \\ \tan C = (x+y)/h \ \\ y = h \cdot \ \tan(C)-x = 11 \cdot \ \tan(1.3679)-24 \doteq 29.4762 = 29.5 \ \text { m }$

Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Be the first to comment!

#### Following knowledge from mathematics are needed to solve this word math problem:

Do you have a linear equation or system of equations and looking for its solution? Or do you have quadratic equation? Do you want to convert length units? Pythagorean theorem is the base for the right triangle calculator. See also our trigonometric triangle calculator.

## Next similar math problems:

1. Ratio iso triangle
The ratio of the sides of an isosceles triangle is 7:6:7 Find the base angle to the nearest answer correct to 3 significant figure.
2. Mast
Mast has 17 m long shadow on a slope rising from the mast foot in the direction of the shadow angle at angle 9.3°. Determine the height of the mast, if the sun above the horizon is at angle 44°30'.
3. Steeple
Steeple seen from the road at an angle of 75°. When we zoom out to 25 meters, it is seen at an angle of 20°. What is high?
4. Right triangle
Calculate the missing side b and interior angles, perimeter and area of ​​a right triangle if a=10 cm and hypotenuse c = 16 cm.
5. 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.
6. Two forces
Two forces with magnitudes of 25 and 30 pounds act on an object at angles of 10° and 100° respectively. Find the direction and magnitude of the resultant force. Round to two decimal places in all intermediate steps and in your final answer.
7. Church tower
Archdeacon church in Usti nad Labem has diverted tower by 186 cm. The tower is 65 m high. Calculate the angle by which the tower is tilted. Result write in degree's minutes.
8. Trigonometric functions
In right triangle is: ? Determine the value of s and c: ? ?
9. Right
Determine angles of the right triangle with the hypotenuse c and legs a, b, if: ?
Between cities A and B is route 13 km long of stúpanie average 7‰. Calculate the height difference of cities A and B.
11. Angle between lines
Calculate the angle between these two lines: ? ?