Question

The students in Miss Collins class used a survey or’s measuring device to find the angle from their location to the top of a building they also measured the distance from the bottom of the building. the diagram shows the angle measure in the distance.

To the nearest foot, what is the height of the building?
A. 105ft
B. 116ft
C. 32ft
D. 54ft
(Image attached)

Answer 1

The height of the building = 105 feet ⇒ answer (A)

Explanation:

* To find the height of the building use the trigonometry functions

- Lets consider the height (h) of the building as a side of right angle triangle

and the other side is the distance from the bottom of the building

- Now we have right angle triangle one of its acute angle is 59°

- The length of one leg of the right angle = 63 feet

- We have the adjacent side of angle 59°

- we need to find the opposite side of angle (h)

∴ Lets use the function tan to find h

∵ tanФ = opposite to Ф/adjacent to Ф

∵ Ф = 59°

∵ The length of the side adjacent to Ф = 63 feet

∴ tan59 = h/63 ⇒ by using cross multiplication

∴ h = 63 × tan 59 = 104.849 ≅ 105 feet

∴ The height of the building = 105 feet answer (A)

Answer 2

A

Explanation:

We can use trigonometric ratios to solve this.

With respect to the angle given, the building's height is the side that is "opposite".

Also, the given length of 63 feet is the "adjacent" side with respect to the angle given.

Which trigonometric ratio relates "opposite to adjacent" side?

It is TAN.

Now, let's write the ratio and solve for the height of the building (let h be height of the building). We have:

`Tan(\theta)=(Opposite)/(Adjacent)\\Tan(59)=(h)/(63)\\h=Tan(59)*63\\h=104.85`

Rounding this, we get h = 105 feet, correct answer A