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MrRissso [65]
3 years ago
7

Engineers and surveyors often determine distances that cannot be measured directly by using similar triangles like the ones show

n below.
Using the information from the drawing, which of these is closest to the distance from Point A on one bank to Point E on the opposite bank?


A.59 feet
B.102 feet
C.118 feet
D.139 feet

Mathematics
1 answer:
ZanzabumX [31]3 years ago
4 0

Answer:

102 ft.

Step-by-step explanation:

See the diagram attached.

From right triangle Δ ADC,  

\sin 30 = \frac{DC}{AC} = \frac{80}{AC}

⇒ AC = 160 ft. {Since \sin 30 = \frac{1}{2} }

Now, given that BC = 42 ft.

Hence, AB = AC - BC = 160 - 42 = 118 ft.

Now, from right triangle Δ AEB we can write

\cos 30 = \frac{AE}{AB} = \frac{AE}{118}

⇒ AE = 118 \cos 30 = 102.19 ft ≈ 102 ft.

Therefore, the closest distance from point A on one bank to point E on the opposite bank is 102 ft. (Answer)

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