Question

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

Answer 1

102 ft.

Explanation:

See the diagram attached.

From right triangle Δ ADC,

`\sin 30 = (DC)/(AC) = (80)/(AC)`

⇒ AC = 160 ft. {Since
`\sin 30 = (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 = (AE)/(AB) = (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)