From a point on the ground the angle of elevation of the top of a tower is x°. Moving 150 meters away from that point the angle of elevation was found to be y° .If tan x=3/4 and tan y=5/7 find the height of the tower.

2250m

Step-by-step explanation:

Step 1

Since

Hence,

tan x = 3/4

tan y=5/7

tan x = BA/ CA where BA = height and CA = distance

3/4 = h/ d

4h = 3d

h = 3d/4 Equation 1

tan y = BA / DA + 150m

5/7 = h/d + 150

7 × h = 5(d + 150)

7h = 5d + 750 Equation 2

Since h = 3d/4

7(3d/4) = 5d + 750

21d/4 = 5d + 750

Multiply both sides by 4

21d = 4(5d + 750)

21d = 20d + 3000

21d -20d = 3000

d = 3000

Distance (d) = 3000m

Substitute 3000m for d in equation 1

h = 3d/4

h = 3 × 3000/4

h = 2250m

Step-by-step explanation:

We have:

By definition of tangent, we have:

Therefore we have the system of equations:

From (1)

            cross multiply

        divide both sides by 3

Substitute it to (2):

           cross multiply

        subtract 20AB from both sides

Such a tower height is rather impossible, but this is the solution.

i think there was a typo. you wrote pat brings 3 quarts of ice-cream to the party. each serving of ice-cream is 1 6 quart. how many total servings of ice-cream does pat bring to the party? i think the bold is supposed to be 1/6. so 1 quart of ice cream = 6 servings. 6 * 3 = 18.