Mathematics, 09.12.2019 07:31 Arielledt10

Aperson is standing on a cliff that is 200ft above a body of water. the person looks
down at an angle of depression of 35° at a sailboat. then the person looks at a yacht
that is further out at an angle of depression of 12°. what is the distance (in feet)
between the sailboat and the yacht? (round to the nearest foot)

Answers: 1

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Answer from: snikergrace

The distance between the sailboat and the yacht is 655 ft

Step-by-step explanation:

Trigonometric Relations

There are situations where the definitions of the sine, cosine, and tangent of an angle are useful to compute lengths, angles, areas, and other geometric variables. If the situation involves right triangles (with one angle of 90°), there is a hypotenuse and two legs, and this relation holds

$\displaystyle \tan \alpha=\frac{opposite\ leg}{adjacent\ leg}$

It's also important to remember that if one line crosses another line, then the opposite angles are equal

The situation described in the question can be pictured in the figure below. For ease of construction and calculations, both angles of depression were translated to their equivalent places inside of both triangles. Applying the relation of the tangent, we can say

$\displaystyle \tan 35^o=\frac{200}{AS}$

Solving for AS

$\displaystyle AS=\frac{200}{\tan 35^o}=\frac{200}{0.7}=286\ ft$

For the other angle

$\displaystyle \tan 12^o=\frac{200}{AY}$

Solving for AY

$\displaystyle AY=\frac{200}{\tan 12^o}=\frac{200}{0.2126}=941\ ft$

Since AY=AS+SY

$SY=941\ ft-286\ ft=655\ ft$

The distance between the sailboat and the yacht is 655 ft

Aperson is standing on a cliff that is 200ft above a body of water. the person looks down at an angl

Answer from: brandonkelly104

The distance between the sailboat and the yacht can be determine by using trigonometry relation. In the given situation we will use sine, cosine, tangent formula to compute angle, length and area.

The distance between the sailboat and the yacht is $655\:\rm feet$ .

Given:

The cliff height is $200\:\rm ft$ .

The angle of depression is $35^{\circ}$ .

The below figure shows the given situation.

Consider the triangle $\Delta ASB$ , write the formula for tan .

$tan35^{\circ} =\frac{AB}{AS}\\tan35^{\circ}=\frac{200}{AS}\\0.7= \frac{200}{AS}\\AS=286 \:\rm ft$

Consider the triangle $\Delta AYB$ , write the formula for tan .

$tan12^{\circ} =\frac{AB}{AY}\\tan12^{\circ}=\frac{200}{AY}\\0.2126= \frac{200}{AY}\\AY=941 \:\rm ft$

From the figure, calculate the value of .

$AY=AS+SY\\941\:\rm ft=286\:\rm+SY\\SY=655\:\rm ft$

The distance between the sailboat and the yacht is $SY=655\:\rm feet$ .

Learn more about height and distance here:

link

Answer from: Quest

step-by-step explanation:

step 1: solve one of the equations for one of the variables. let's solve the first equation for y:

step 2: substitute that equation into the other equation, and solve for x.

step 3: substitute x = 4 x = 4 x=4 into one of the original equations, and solve for y.

Answer from: Quest

answer: on graphs, the open and closed circles, or vertical asymptotes drawn as dashed lines us identify discontinuities.

as before, graphs and tables allow us to estimate at best.

when working with formulas, getting zero in the denominator indicates a point of discontinuity.

when working with piecewise-defined functions, check for discontinuities at the transition points where one piece ends and the next begins.

step-by-step explanation:

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