Mast

Mast has 13 m long shadow on a slope rising from the mast foot in the direction of the shadow angle at angle 13.3°. Determine the height of the mast, if the sun above the horizon is at angle 45°12'.

Result

v =  17.65 m

Solution:

$l=13 \ \text{m} \ \\ A=13.3 \ ^\circ \ \\ B=45.2 \ ^\circ \ \\ \ \\ \sin(A)=\dfrac{ h }{ l } \ \\ h=l \cdot \ \sin A ^\circ =l \cdot \ \sin 13.3^\circ \ =13 \cdot \ \sin 13.3^\circ \ =l \cdot \ 0.23005=2.99065 \ \\ \ \\ x=l \cdot \ \cos A ^\circ =l \cdot \ \cos 13.3^\circ \ =13 \cdot \ \cos 13.3^\circ \ =l \cdot \ 0.973179=12.65133 \ \\ \ \\ \tan(A+B)=\dfrac{ h+v }{ x } \ \\ v=x \cdot \ \tan(( A+B) ^\circ \rightarrow\ \text{rad}) - h=x \cdot \ \tan(( A+B )^\circ \cdot \ \dfrac{ \pi }{ 180 } \ ) - h=12.6513253461 \cdot \ \tan(( 13.3+45.2 )^\circ \cdot \ \dfrac{ 3.1415926 }{ 180 } \ ) - 2.99064658345=17.65444=17.65 \ \text{m}$

Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

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

Be the first to comment!

Tips to related online calculators
Check out our ratio calculator.
Do you want to convert length units?

You need to know the following knowledge to solve this word math problem:

We encourage you to watch this tutorial video on this math problem:

Next similar math problems:

1. Cable car 2
Cable car rises at an angle 41° and connects the upper and lower station with an altitude difference of 1175 m. How long is the track of cable car?
2. One side
One side is 36 long with a 15° incline. What is the height at the end of that side?
3. 30-60-90
The longer leg of a 30°-60°-90° triangle measures 5. What is the length of the shorter leg?
4. Flowerbed
Flowerbed has the shape of an isosceles obtuse triangle. Arm has a size 5.5 meters and an angle opposite to the base size is 94°. What is the distance from the base to opposite vertex?
5. Tree
How tall is the tree that observed in the visual angle of 52°? If I stand 5 m from the tree and eyes are two meters above the ground.
6. 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?
7. Maple
Maple peak is visible from a distance 3 m from the trunk from a height of 1.8 m at angle 62°. Determine the height of the maple.
8. Median
The median of the triangle LMN is away from vertex N 84 cm. Calculate the length of the median, which start at N.
9. Obtuse angle
The line OH is the height of the triangle DOM, line MN is the bisector of angle DMO. obtuse angle between the lines MN and OH is four times larger than the angle DMN. What size is the angle DMO? (see attached image)
10. Cosine
The point (8, 6) is on the terminal side of angle θ. cos θ = ?
11. Building
The building I focused at an angle 30°. When I moved 5 m building I focused at an angle 45°. What is the height of the building?
12. 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?
13. Reference angle
Find the reference angle of each angle:
14. High wall
I have a wall 2m high. I need a 15 degree angle (upward) to second wall 4 meters away. How high must the second wall?
15. Sines
In ▵ ABC, if sin(α)=0.5 and sin(β)=0.6 calculate sin(γ)
16. Height 2
Calculate the height of the equilateral triangle with side 38.
17. Center traverse
It is true that the middle traverse bisects the triangle?