Two buildings are 100 metres apart. Building 1 is shorter than Building 2. From the edge of the roof of Building 1 closest to Building 2, the angle of elevation to the top of Building 2 is 25.0∘. From that same point, the angle of depression to the bottom of Building 2 is 30.0∘. Determine the height of Building 2 to the nearest metre.

height of building 2 ≈ 104 m(nearest metre)

Step-by-step explanation:

The angle of elevation from the top of the shorter building to the top of the taller building is 25°.The angle of depression from the top of the shorter building to the base of the taller building is 30°. The height of building 2 (taller building) is the sum of the height of building 1 plus the height from the roof of building 1 where the angle of elevation was measured to the topmost layer of building 2.

The height of building 1 can be calculated using the tangential properties of the right angle triangle formed. The adjacent side is 100 m while the opposite side is the height of building 1.

tan 30° = opposite/adjacent

tan 30° = height of building 1/100

height of building 1 = 100 tan 30°

height of building 1 = 100 × 0.57735026919

height of building 1 = 57.735026919

height of building 1 = 57.74 m

The angle of elevation from the top of building 1 to the top of building 2 forms a right angle triangle .

using tangential ratio

tan 25° = opposite/adjacent

tan 25° = height from the top of building 1 to the topmost layer of building 2/100

height from the top of building 1 to the topmost layer of building 2 = 100 tan 25°

height from the top of building 1 to the topmost layer of building 2 = 100 × 0.46630765815

height from the top of building 1 to the topmost layer of building 2 = 46.6307658155

height from the top of building 1 to the topmost layer of building 2 = 46.63 m

Height of building 2 = 46.63  + 57.74 = 104.37  m

height of building 2 ≈ 104 m

b is the answer that makes most sense

step-by-step explanation:

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form