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To find the distance across a river, a surveyor choose points A and B, which are 230 ft apart on one side of the river. She then chooses a reference point C on the opposite side of the river and finds that


How do I solve this?


I had side a be 226.71 ft long, but I don’t know how to find the height of the triangle.


Somebody please correct me and help me by giving a step by step so I can see where I might have went wrong!

To find the distance across a river a surveyor choose points A and B which are 230 ft apart on one side of the river She then chooses a reference point C on the class=


Answer :

The approximate distance from A to C is 226.71 feet.

The distance across the river is 222.54 feet.

How to find the side of a triangle?

To find the distance across a river, a surveyor choose points A and B, which are 230 ft apart on one side of the river. She then chooses a reference point C on the opposite side of the river and find that ∠BAC ≈ 79 degrees and ∠ABC ≈ 50 degrees.

The distance A to C can be found as follows:

sine law can be use to find AC.

a / sin A = b / sin B = c / sin C

Therefore,

230 / sin 51° = AC / sin 50

cross multiply

230 sin 50° = AC sin 51°

176.190221917 = 0.77714596145 AC

divide both sides by 0.77714596145

AC = 176.190221917 / 0.77714596145

AC = 226.714453469

AC = 226.71 feet

The distance across the river is the height of the triangle.

Therefore,

using trigonometric ratios,

sin 79° = opposite / hypotenuse

sin 79° = h / 226.71

cross multiply

h = 226.71 sin 79°

h = 226.71 × 0.98162718344

h = 222.544698759

h = 222.54 feet.

learn more on triangle here: https://brainly.com/question/12472542

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