Respuesta :
Answer:
514 m = width of the river to the nearest meter
Step-by-step explanation:
You must memorize the definitions of the trig functions and then these types of problems are easy.
You have a right triangle where the 100 m is the adjacent side to the 79° angle. You are looking for the side opposite the 79° angle. So, you need to use the tan function which is defined as opposite side/adjacent side
Let x = the length of the opposite side (width of river)
Tan 79 = x/100
100 tan 79 = x
x = 514 m = width of the river to the nearest meter
The tangent or tanθ in a right angle triangle is the ratio of its perpendicular to its base. The width of the river is 514.455 meters.
What is Tangent (Tanθ)?
The tangent or tanθ in a right angle triangle is the ratio of its perpendicular to its base. it is given as,
[tex]\rm Tangent(\theta) = \dfrac{Perpendicular}{Base}[/tex]
where,
θ is the angle,
Perpendicular is the side of the triangle opposite to the angle θ,
Base is the adjacent smaller side of the angle θ.
As it is given that you walk 100 meters to the right of the stake and measure a 79° angle between the stake and the boulder. Therefore, using the tangent angle the width of the river can be written as,
[tex]\rm Tangent(\theta) = \dfrac{Perpendicular}{Base}\\\\\\\rm tan(79^o) = \dfrac{\text{Width of the river}}{100\ meter}\\\\\\\text{Width of the river} = tan(79^o) \times 100 = 514.455\ meters[/tex]
Hence, the width of the river is 514.455 meters.
Learn more about Tangent (Tanθ):
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