SSA and geometry

The distance between the points P and Q was 356 m measured in the terrain. The PQ line can be seen from the viewer at a viewing angle of 107° 22 '. The observer's distance from P is 271 m. Determine the viewing angle of P and observer.


Q =  46.597 °


R=107+2260=322130107.3667  r=356 m q=271 m  sin(Q)sin(R)=qr  s=sin(Q) s=qr sin(R rad)=qr sin(R π180 )=271356 sin(107.36666666667 3.1415926180 )=0.72653  Q=180πarcsin(s)=180πarcsin(0.7265)46.596646.597463548"R=107+\dfrac{ 22 }{ 60 }=\dfrac{ 3221 }{ 30 } \doteq 107.3667 \ ^\circ \ \\ r=356 \ \text{m} \ \\ q=271 \ \text{m} \ \\ \ \\ \dfrac{ \sin(Q) }{ \sin(R) }=\dfrac{ q }{ r } \ \\ \ \\ s=\sin(Q) \ \\ s=\dfrac{ q }{ r } \cdot \ \sin( R ^\circ \rightarrow\ \text{rad})=\dfrac{ q }{ r } \cdot \ \sin( R ^\circ \cdot \ \dfrac{ \pi }{ 180 } \ )=\dfrac{ 271 }{ 356 } \cdot \ \sin( 107.36666666667 ^\circ \cdot \ \dfrac{ 3.1415926 }{ 180 } \ )=0.72653 \ \\ \ \\ Q=\dfrac{ 180^\circ }{ \pi } \cdot \arcsin(s)=\dfrac{ 180^\circ }{ \pi } \cdot \arcsin(0.7265) \doteq 46.5966 \doteq 46.597 ^\circ \doteq 46^\circ 35'48"

Try calculation via our triangle calculator.

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...):

Showing 0 comments:
1st comment
Be the first to comment!

Tips to related online calculators
Need help calculate sum, simplify or multiply fractions? Try our fraction calculator.
Check out our ratio calculator.
See also our trigonometric triangle calculator.
Try conversion angle units angle degrees, minutes, seconds, radians, grads.

Next similar math problems:

  1. Parametric equation
    line Find the parametric equation of a line with y-intercept (0,-4) and a slope of -2.
  2. Effective and mean voltage
    serial-parallel A voltage divider consisting of resistors R1 = 103000 Ω and R2 = 197000 Ω is connected to the ideal sine wave voltage source, R2 is connected to a voltmeter which measures the mean voltage and has an internal resistance R3 = 200300 Ω, the measured value i
  3. A triangle
    triangle1_1 A triangle has an angle that is 63.1 other 2 are in ratio of 2:5 What are the measurements of the two angles?
  4. Largest angle of the triangle
    obtuse_triangle Calculate the largest angle of the triangle whose sides have the sizes: 2a, 3/2a, 3a
  5. Median
    tazisko The median of the triangle LMN is away from vertex N 84 cm. Calculate the length of the median, which start at N.
  6. Theorem prove
    thales_1 We want to prove the sentence: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?
  7. Angles
    triangle_1111_1 In the triangle ABC, the ratio of angles is: a:b = 4: 5. The angle c is 36°. How big are the angles a, b?
  8. Isosceles triangle
    math_fun_1 What are the angles of an isosceles triangle ABC if its base is long a=5 m and has an arm b=4 m.
  9. Ladder slope
    rebrik33 What is the slope of a ladder 6.2 m long and 5.12 m in height.
  10. Trigonometry
    sinus Is true equality? ?
  11. Two triangles SSA
    ssa Two triangles can be formed with the given information. Use the Law of Sines to solve the triangles. A = 59°, a = 13, b = 14
  12. Reference angle
    anglemeter Find the reference angle of each angle:
  13. Ratio 11
    zlomky_7 Simplify this ratio 10 : 1/4
  14. Angles by cosine law
    357_triangle Calculate the size of the angles of the triangle ABC, if it is given by: a = 3 cm; b = 5 cm; c = 7 cm (use the sine and cosine theorem).
  15. Third member
    seq_6 Determine the third member of the AP if a4=93, d=7.5.
  16. Rhomboid
    triangle-ssa The dimensions of the rhomboid sides are a= 5cm, b = 6 cm and the size of the angle at the vertex A is 60°. What is the length of side AC?
  17. Right triangle
    rebrik_7 Ladder 16 feet reaches up 14 feet on a house wall. The 90-degree angle at the base of the house and wall. What are the other two angles or the length of the leg of the yard?