The angles of depression of two ships from the top of the light house are 45° and 30° towards east. If the ships are 200 m apart, find the height of the lighthouse. please answer with figure.

273 meters

Step-by-step explanation:

See image attached for the diagram I used to represent this scenario.

The distance between the ships, at angles 30 and 45, is 200 meters. The distance between the left ship and the lighthouse is x meters.

We can use trigonometric ratios to solve this problem. We can use the tangent ratio to create an equation with the two angles.

Let's take these two equations and solve for x in both of them.

tan(45) = 1, so we can rewrite this equation.

Multiply x to both sides of the equation.

Multiply x + 200 to both sides and divide h by tan(30).

Subtract 200 from both sides of the equation.

Simplify h/tan(30).

Take Equation I and Equation II and set them equal to each other.

Subtract √3 h from both sides of the equation.

Factor h from the left side of the equation.

Divide both sides of the equation by 1 - √3.

Rationalize the denominator by multiplying the numerator and denominator by the conjugate.

Simplify this equation.

The height of the lighthouse is about 273 meters.

Step-by-step explanation:

Please refer to the attachment.

In the attachment, h is the height of the lighthouse and x is the distance from the lighthouse to Ship A.

Since the angle of depression from the top of the lighthouse to Ship A is 45°, this means that the angle of elevation from Ship A to the top of the lighthouse is 45°.

Likewise, the angle of elevation from Ship B to the top of the lighthouse is 30°.

So, we will form two right triangles: the smaller, 45-45-90 triangle, and the larger 30-60-90 triangle.

Remember that in 45-45-90 triangles, the two legs are congruent.

Therefore, we can write that:

Next, in 30-60-90 triangles, the longer leg is always √3 times the shorter leg.

In our 30-60-90 triangle, the shorter leg is given by:

And the longer leg is given by:

So, the relationship between the shorter leg and longer leg is:

And since we know that h is equivalent to x, we can write:

Now, we just have to solve for h. We can subtract h from both sides:

Factoring out the h yields:

Therefore:

Approximate. So, the height of the lighthouse is approximately:

9) i can't see the angle so whatever it is just do this: cos(angle) x hypotenuse and then use that answer and they hypotenuse and plug it into this: (answer you just got)^2 + b^2 = (hypotenuse)^2. the first answer will be the answer of the adjacent side and the second answer after this equation will be the opposite side.

10) y = 14 x = √147 or 12.12435565

11) x = 4.8

12) x = 4.2

13) x = 9.3

14) pq: 13.2

qr : 17.6

angle p: 53º

15) angle c: 54.3º

angle a: 35.7º

16) h = 21040

v = 1841

step-by-step explanation:

10) 7/sin(30) = 14 = y

7^2 + b^2 = 14^2

49 + b^2 = 196

b^2 = 196 - 49

√b^2 = √147

x = √147

11) cos(70) x 14 = 4.788282007

x = 4.8

12) tan(25) x 9 = 4.196768923

x = 4.2

13) sin(31) x 18 = 9.270685348

x = 9.3

14) pq: sin(37) x 22 = 13.23993051

pq: 13.2

qr: cos(37) x 22 = 17.56998122

qr : 17.6

angle p: 180 - (37 + 90) = 53º

15) cos-1(7/12) = 54.31466529

angle c: 54.3º

angle a: 180 - (90 + 54.31466529) = 35.68533471

angle a: 35.7º

16) 4 x 5280 = 21120

cos(5) x 21120

h = 21039.63202

h = 21040

sin(5) x 21120

v = 1840.729287

v = 1841