Answer:
407.22 foot is the boat from the base of the lighthouse
Step-by-step explanation:
Given the statement: An observer on top of a 50-foot tall lighthouse sees a boat at a 7° angle of depression.
Let x foot be the distance of the object(boat) from the base of the lighthouse
Angle of depression = 
[Alternate angle]
In triangle CAB:
To find AB = x foot.
Using tangent ratio:


Here, BC = 50 foot and 
then;

or


Simplify:
AB = x = 407.217321 foot
Therefore, the boat from the base of the light house is, 407.22'
Answer:
11.2 miles
Step-by-step explanation:
We can create a triangle from the information given.
<u>We can call the starting point (0,0) in the coordinate system.</u>
- <u>10 mi east</u> - 10 miles to the right. then,
- <u>5 mi north</u> - 5 miles above
<em><u>See the attached picture. The direct distance is labeled as x.</u></em>
Now we need to find x using pythagorean theorem.
Pythagorean Theorem = leg²+leg²=hypotenuse²
Solving for x:

<em>Rounding to nearest tenth, we have </em><em>11.2 miles</em>
Answer: 1/2
Step-by-step explanation:
1) Put the equation into y=kx form
- add 4x to both sides
- divide by 8 on both sides to get y=1/2x
2) k is the constant of proportionality