A point on the ground is 50 feet from my house. The angle of elevation to the top of the house is 48∘. Find the height of the ho
use to the nearest tenth.
1 answer:
You might be interested in
Answer:
A) S = f(d) = √(36 + d²)
B) d = g(t) = 30t
C) f o g = √(36 + 900t²)
Explanation:
A) Express the distance s between the lighthouse and the ship as a function of d, the distance the ship has traveled since noon;that is, find f so that s = f(d)
Refer to the attached image and observe that ship starts moving from point I towards point N which represents the position of ship at noon.
From point I to point N ship covers the distance d.
From point I to point L (lighthouse) the distance is S.
A triangle is formed and we want the distance S so we will apply the Pythagorean theorem
IL² = NL² + IN²
S² = 6² + d²
S = √(36 + d²)
Therefore, the function is S = f(d) = √(36 + d²)
B) Express d as a function of t, the time elapsed since noon;that is, find g, so that d = g(t)
Since the ship is moving at a speed of 30 km/h and let t represents the time taken to move from I to N then
d = 30t
or
d = g(t) = 30t
C) Find f o g. What does this function represent?
Since we have already found f(d) and g(t) we can find f o g.
f(d) = √(36 + d²) and d = g(t) = 30t
substitute d = g(t) = 30t into f(d)
f o g = √(36 + (g(t))²)
f o g = √(36 + (30t)²)
f o g = √(36 + 900t²)
This function simply represents the distance from point I to point N to point L which is the longer distance from the initial position of ship to the lighthouse.
For this case we can use the law of the sine to solve the problem.
We have then:
From here, we clear the value of x.
We have then:
Rewriting we have:
Answer:
The angle R is given by:
x = 68 degrees
option B
We have then:
From here, we clear the value of x.
We have then:
Rewriting we have:
Answer:
The angle R is given by:
x = 68 degrees
option B