The tower is 700 meters high. suppose a building is erected such that the base of the building is on the same plane as the base of the tower, the angle of elevation from the top of the building to the top of the tower is 80.38° and the angle of depression from the top of the building to the foot of the tower is 65.05°. how high would the building have to be?

The answer is 187.25m.

Step-by-step explanation:

Have a look at the (very quick) picture I drew of the situation. We have the tower (T) and the building (B). The tower is 700m tall and the angles of elevation and depression as described in the question are shown in the picture.

You'll notice that (blue) triangles can be formed when those angles are sketched in. There's a big scalene triangle, △ABC, and two smaller right-angled triangles, △ADB and △BDC. The question wants the height of the building, which corresponds to the green line (DC). We have sides and we have angles, so sounds like a job for trigonometry.

We know that AC = 700. Therefore, AD + DC = 700, so AD = 700 - DC (1). We have 1 equation but 2 unknowns, so we need to develop a second equation so we have a solvable system. We can get that second equation using the small triangles:

For △ADB: tan80.38 = AD/BD → BD = AD/tan80.38 (2)

For △BDC: tan65.05 = DC/BD → BD = DC/tan65.05 (3)

Yes a third variable (BD) has been introduced, but notice that it appears in both equations and we can rearrange them to isolate it. This is why I used tan instead of cos or sin - tan is the only one of the 3 that shares that side for both triangles. After the rearranging we get equations (2) and (3), which can be set equal to each other to get rid of that third variable:

AD/tan80.38 = DC/tan65.05 (4)

We can now sub (1) into (4) and solve for DC:

(700 - DC)/tan80.38 = DC/tan65.05

(700 - DC)tan65.05 = DCtan80.38

700tan65.05 - DCtan65.05 = DCtan80.38

DCtan80.38 + DCtan65.05 = 700tan65.05

DC(tan80.38 + tan65.05) = 700tan65.05

DC = 700tan65.05/(tan80.38 + tan65.05)

DC = 187.25

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions

the system of inequity is

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

the solid line passing through the points (0,4) and (4,0).

the related equation of solid line is .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

the related equation of dashed line is

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be . the required inequality is

similarly, check the second related equation.

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is