OT is a vertical mast of height h. From A, a m due south of O, the angle of elevation of T is 30 degree. If B is a point 2a m from A, on a bearing of 060 degree, find the angle of elevation of T from B.

Question

OT is a vertical mast of height h. From A, a m due south of O, the angle of elevation of T is 30 degree. If B is a point 2a m from A, on a bearing of 060 degree, find the angle of elevation of T from B.

Answer 1

tan 30 = h/a

tan T = h/2a

tan T = (1/2) tan 30

T = 8.21 degrees

Answer 2

note: AB=2a m, AO=a m,OB=? And angle OAB=60 degree

Answer 3

So we are looking at a 3-D diagram?

Triangle AOT is a 30-60-90° triangle with sides in the ratio of 1:√3:2
so h:a:AT = 1:√3:2
h/1 = a/√3
h = a/√3
AT/2 = a/√3
AT = 2a/√3 -- may not need this

in triangle AB , the ground plane ...
we can use the cosine law to find OB
OB^2 = a^2 + 4a^2 - 2(a)(2a)cos60
= 5a^2 - 4a^2(1/2)
= 3a^2
OB = √3a

now in triangle BOT
tan (OBT) = (a/√3) / (√3a)
= 1/3
angle B)t = appr 18.4°

check my arithmetic

Answer 4

that's great Reiny, you are perfectly correct. Thank you somuch

Answer 5

To find the angle of elevation of T from B, we can use trigonometry to calculate the height of OT, and then use that information to determine the angle of elevation.

Let's break down the problem step by step:

Step 1: Calculating the height of OT
Given that point A is located a distance of "a" meters directly south of O, we need to find the height of OT, which is represented by "h".

Since the angle of elevation of T from A is 30 degrees, we can use trigonometry to find the height:
tan(30°) = h / a
h = a * tan(30°)

Step 2: Calculating the distance from B to T
To calculate the distance from B to T, we need to determine the horizontal distance from A to T and add it to the horizontal distance from A to B.

The horizontal distance from A to T (AT) is given by:
AT = a * cos(30°)

The horizontal distance from A to B (AB) is 2a meters, as mentioned in the question.

So, the total horizontal distance from B to T (BT) equals:
BT = AT + AB
BT = a * cos(30°) + 2a

Step 3: Calculating the angle of elevation of T from B
The angle of elevation of T from B can be found by using the height of OT (h) and the horizontal distance from B to T (BT). We can then use the tangent function:

tan(angle of elevation from B) = h / BT
angle of elevation from B = arctan(h / BT)

Substituting the values calculated above:
angle of elevation from B = arctan(a * tan(30°) / (a * cos(30°) + 2a))

Simplifying further, we get:
angle of elevation from B = arctan(tan(30°) / (cos(30°) + 2))

Therefore, to find the angle of elevation of T from B, you can use the formula:
angle of elevation from B = arctan(tan(30°) / (cos(30°) + 2))