A rocket is launched from the space coast of Florida and can be seen from local schools. The angles of elevation from western high school and pine high school are 41 degrees and 23 degrees respectively. If the schools stands 512 miles apart , how far is the rocket from pine high school

distance of the rocket from the pine high school ≈ 344 miles

Step-by-step explanation:

The illustration forms a triangle with 2 right angle triangle in it. The western high school angle of elevation  is 41° and the pine high school angle of elevation is 23°. The distance between the 2 school is 512 miles .The distance of the rocket from the pine school is the adjacent side of one of the right angle triangle .

The full triangle has angle of 23°, 41° and the last angle will be 180 - 23 - 41 = 116°. The hypotenuse side of the right angle triangle representing the pine high school triangle can be solved using sine formula.

p/sin 41° = 512/sin 116°

p/0.65605902899 = 512/0.89879404629

cross multiply

0.89879404629 p = 335.902222843

divide both sides by 0.89879404629

p = 335.902222843 /0.89879404629

p = 373.725464949

p ≈ 373.70 miles

using cosine ratio the adjacent side of the triangle can be found.

cos 23° = adjacent/hypotenuse

cos 23° = adj/373.70

cross multiply

adjacent = 0.92050485345  × 373.70

adjacent = 343.992663735

distance of the rocket from the pine high school = 343.992663735

distance of the rocket from the pine high school ≈ 344 miles

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

step-by-step explanation:

given   that triangle lno is congruent to triangle lnm.

we have to fill up the blanks in the given question.

according to above order of congruency   kept in mind we can say that

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

ln ≅ ln due to common in both.

hence, by sas congruency,

the side angle side rule   states that if two sides and the included angle of one triangle are congruent to another triangle, then these two triangles are congruent.