Question

Kayson is looking at two buildings, building A and building B, at an angle of elevation of 73°. Building A is 30 feet away, and building B is 35 feet away. Which building is taller and by approximately how many feet?

Answer 1

welcome to qc and let me do some math

Answer 2

Thanks and ok

Answer 3

do you have answer choices?

Answer 4

Building A; it is around 16.35 feet taller than building B
Building A; it is around 114.48 feet taller than building B
Building B; it is around 16.35 feet taller than building A
Building B; it is around 114.48 feet taller than building A

Answer 5

whitch 2 can you cross off?

Answer 6

Hey @DanielRichter let's first draw an image so we can solve this question

Answer 7

OK

Answer 8

Does that image make sense?

(It's obviously not to scale)
But we're looking at two buildings from an angle of 73 degrees

Building A is 30 feet away
Building B is 35 feet away

we want to know how much taller the second building is from the first

Answer 9

So we need to first find the height of building A and then building B

our answer will be
height of building B minus height of building A

do you know which trigonometric function we would need to use?

we have the angle and we have the adjacent side
we're trying to find the opposite side

Answer 10

Here's probably a better image

Answer 11

Tangent

Answer 12

Good! So let's first figure out the height of building A

we're looking for the side opposite
we know the angle is 73
and the adjacent side is 30

can you set it up to calculate the length of the opposite side?

tan \(\theta\) = opposite/ adjacent

Answer 13

yes and it is 98.13

Answer 14

Perfect! Now calculate the length of building B the same way

but remember, this time the adjacent side is 35!
The angle stays the same at 73

Answer 15

114.48

Answer 16

Good! So that's the height of building B

now they want to know which building is taller
(obviously building B)

and by how much

so now you just calculate the difference

114.48 - 98.13 = ?

Answer 17

16.35

Answer 18

You got it!

Answer 19

thanks so much AZ

Answer 20

Of course, it was my pleasure!