From the top of a building, the angle of elevation to the top of a nearby building is 28° and the angle of depressions to the bottom of the nearby building is 48°. The distance between the two buildings is 50m, as shown in the diagram below. What is the height of the taller building, to the nearest tenth of a metre?

Step-by-step explanation:

The idea here is to find the value for x and y, then add them together. See the pic I attached below. We will solve for side x first.

Side s is across from the reference angle of 48 degrees; side measuring 50 m is adjacent to the reference angle 48 degrees. Therefore, we will use the tangent ratio to solve for x:

and

50tan(48) = x so

x = 55.53m

Now we will do the same and solve for y. This time the reference angle is 28 degrees. Side y is opposite the reference angle and the side measuring 50 is adjacent to the reference angle, so we will use the tangent ratio again:

and

50tan(28) = y so

y = 26.59. Therefore,

x + y = 55.53 + 26.59 and

the height of the taller building is

82.1 m

3. (5x + 1) - (-10x + 6)

simplify the answer choice. combine like terms. remember to distribute the negative to the terms inside the second parenthesis. also remember that two negatives = one positive, and one of each sign = negative.

- (-10x + 6) = + 10x - 6

simplify. combine like terms:

5x + 1 + 10x - 6

5x + 10x + 1 - 6

15x - 5

∴ it is your answer

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