Find X and Y using the image.

Mathematics

1 answer:

r-ruslan [8.4K]3 years ago

3 0

Answer:

x = 59°

y = 130°

Step-by-step explanation:

Find x:

Recall: the measure of an inscribed angle = ½(measure of intercepted arc), based in the inscribed angles theorem

Therefore,

x = ½(118°)

x = 59°

Find y:

y = 2(180 - (56 + x)) => inscribed angles theorem

Plug in the value of x

y = 2(180 - (56 + 59))

y = 2(180 - 115)

y = 2(65)

y = 130°

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The diagram below shows a student using a clinometer to measure the height of a flagpole. When the student stands 40 feet away f

AVprozaik [17]

The correct answer is the flagpole is <span>33 feet high</span>.

Explanation:
Please refer to the attached picture.

We know:
CD = 40 feet
AC = 5 feet
∠BDC = α = 35°

Using trigonometry, we know that the definition of the tangent of an angle is the ratio between the opposite side and the adjacent side, therefore:
tan α = BC / CD

Solving for BC:
BC = CD · <span>tan α
= 40 </span>· tan (35)
= 28 feet

In order to find the height of the flagpole, we need to add the distance of the clinometer from the ground:
AB = BC + AC
= 28 + 5
= 33

Hence, the flagpole is 33 feet high.