College Trigonometry

Question

The angle of elevations were taken to the top of tall mountain at point A and point B. The angle elevation at point A is 350 and at point B is 600 . The two points are in line with the foot of the mountain. If the distance of point A and B is 40 m, what is the height of the mountain? What is the distance of point B to the foot of the mountain? Show the solution

Answer 1

College Trigonometry: The angle of elevations were taken to the top of tall mountain at point A and point B. The angle elevation at point A is 35⁰ and at point B is 60⁰. The two points are in line with the foot of the mountain. If the distance of point A and B is 40 m, what is the height of the mountain? What is the distance of point B to the foot of the mountain? Show the solution

Detailed Solution

Given/Known: <A = 35⁰,      <B = 60⁰,       AB = 40 m,   h = ?? m x – 40 = ??

Draw the two triangles as instructed above

At Point A: h/x = tan 35⁰ ==> h = x tan 35⁰ <== Equation 1

At Point B: h/(x – 40) = tan 60⁰ ==> h = (x – 40) tan 60⁰ <== Equation 2

Equation 1 = Equation 2

x tan 35⁰ = (x – 40) tan 60⁰

x tan 35⁰ = x tan 60⁰ – 40 tan 60⁰

40 tan 60⁰ = x tan 60⁰ – x tan 35⁰

x(tan 60⁰ – tan 35⁰) = 40 tan 60⁰

x = (40 tan 60⁰)/(tan 60⁰ – tan 35⁰) <== Equation 3

Substitute Equation 3 into Equation 1

h = x tan 35⁰ <== Equation 1

h = (40 tan 60⁰)/(tan 60⁰ – tan 35⁰) * (tan 35⁰)

h = (40 tan 60⁰)(tan 35⁰)/(tan 60⁰ – tan 35⁰) <== Exact height of the mountain – Final Solution

h = 47.01469954 m <==Approximation (Make sure your calculator is in Degree Mode)

x – 40 = (40 tan 60⁰)/(tan 60⁰ – tan 35⁰) – 40 <== Exact distance of point B – Final Solution

x – 40 = 27.14394944 m <==Approximation (Make sure your calculator is in Degree Mode)