The angle of elevation of the top of house from the bottom of a tower 160m high is 26 degree.From the top of the tower the angle of elevation is 24 degree.What is the height of the house if the tower and the house are 50m apart?

tan26/1=opp/adj=he/x

he=xtan26
tan24=he/50
he=50tan24
=50x0.445
=22.25
height of the house=he+he
=160+22.25
=182.25

Well, it seems like we have some angular acrobatics going on here! Let's see if we can solve this height-height conundrum.

First things first, we'll start by using some basic trigonometry. Let's call the height of the house "h". We know that the angle of elevation from the bottom of the tower to the top of the house is 26 degrees, which means:

tan(26) = h / 50

Now, let's move to the top of the tower. The angle of elevation from there to the top of the house is 24 degrees, so we can set up another equation:

tan(24) = (h + 160) / 50

Now, we have a nice little system of equations. Let's solve it and find out the height of the house, shall we?

Solving the first equation for h, we get:

h = tan(26) * 50

Plugging this value of h into the second equation, we get:

tan(24) = (tan(26) * 50 + 160) / 50

Now, time for some calculator magic! Crunch those numbers, and we find that h ≈ 114.03 (rounded to two decimal places).

Therefore, the height of the house is approximately 114.03 meters.

So, the house has got some height to show off along with the tower!

To find the height of the house, we can use trigonometry, specifically the concept of tangent.

Let's denote the height of the house as 'h'.

From the bottom of the tower, the angle of elevation to the top of the house is 26 degrees. This means that the tangent of 26 degrees is equal to 'h' divided by the distance between the tower and the house, which is 50m.

So, we have:

tan(26°) = h / 50

Similarly, from the top of the tower, the angle of elevation to the top of the house is 24 degrees. This means that the tangent of 24 degrees is equal to the height of the tower (160m + 'h') divided by the distance between the tower and the house, which is still 50m.

So, we have:

tan(24°) = (h + 160) / 50

Now, we have two equations with two unknowns ('h' and the angle of elevation) - one equation for each observation.

We can solve these two equations simultaneously to find the value of 'h'.

First, let's rearrange the first equation to solve for 'h':

tan(26°) = h / 50
h = 50 * tan(26°)

Next, let's substitute this expression for 'h' in the second equation:

tan(24°) = (h + 160) / 50
tan(24°) = (50 * tan(26°) + 160) / 50

Now, we can solve this equation to find the value of 'h'.

Using a scientific calculator or an online calculator with trigonometric functions, calculate the value of the right-hand side of the equation:

(50 * tan(26°) + 160) / 50 ≈ 1.416

Therefore, the height of the house, 'h', is approximately 1.416 meters.

i don,t know it

Tan26 = h/50

h = 50*Tan26 = 24.4 m.

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