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

question 1 is 8, question 2 is 9, question 3 is 24

step-by-step explanation:

now, the numbers they give you at the top are the key. from there, you just have to plug and chug! let's try 1, 2, and 3!

key: a=3, b=5, c=6

1. a+5

remember, a=3, so we plug that in to get 3+5=8

2. 15-c

c=6, so we plug that in to get 15-6=9

3. 4b

b=6, so we plug it in to get 4*6=24

time to try the rest on your own! if you put the answers below in a comment, i'll check them for you!

answer is 8x+24

area of vanessa's patio = length × width

given, length = (3x² + 5x + 10)

width = (x² - 3x - 1)

area of vanessa's patio = (3x² + 5x + 10)(x² - 3x - 1)

= 3x²(x² - 3x - 1) + 5x(x² - 3x - 1) + 10(x² - 3x - 1)

= 3x⁴ - 9x³ - 3x² + 5x³ - 15x² - 5x + 10x² - 30x - 10

= 3x⁴ - 4x³ - 8x² - 35x - 10

hence, expression of vanessa's patio = (3x⁴ - 4x³ - 8x² - 35x - 10)