The tangent of the angle gives the ratio of the height of the lighthouse to the boat's distance
.. tan(angle of depression) = (lighthouse height)/(boat distance)
Then the distance to the boat is
.. boat distance = (lighthouse height)/tan(angle of depression)

We want to find the difference between two distances, so
.. boat travel = (lighthouse height)*(1/tan(first angle) -1/(tan(second angle))
.. = (200 ft)*(1/tan(17°31') -1/tan(46°41'))
.. ≈ 445.10 ft

4 0

4 years ago

In ∆ABC the angle bisectors drawn from vertices A and B intersect at the point D. Find m∠ADB if

Svetllana [295]

Answer: ∠ABD = $\bold{\frac{1}{2}}$ ∠C

<u>Step-by-step explanation:</u>

$\angle A + \angle B + \angle C = 180^o\\\\\dfrac{1}{2}\angle A+\dfrac{1}{2}\angle B+\angle D=180^o\\\\\\\text{Solve the system by multiplying the second equation by -2}\\\angle A + \angle B + \angle C = 180^o\\\underline{-\angle A - \angle B - 2\angle D = -180^o}\\.\qquad \qquad \quad \angle C-2\angle D=0\\.\qquad \qquad \qquad \qquad \angle C=2\angle D\\.\qquad \qquad \qquad \quad \dfrac{1}{2}\angle C=\quad \angle D\\$

8 0

3 years ago

Plz help when you see this

kolezko [41]

Answer:

126

Step-by-step explanation:

angle ZWY = 180 - 90 - 63 = 27

Base on the given information, the length of XW is same with the length of ZW, which means they have the same angle.

Quadrangle has angle of 360

360(quadrangle) - 27(ZWY)- 27(XWY) - 90(WZY) - 90(WXY)

= 126

5 0

2 years ago

What’s the amplitude,period,equation of axis, and range for y=3sin[2(x+90)]?

d1i1m1o1n [39]

Answer:

amplitude: 3
period: π
axis: y = 0
range: [-3, +3]

Step-by-step explanation:

The amplitude is the multiplier of the sine function: 3.

The period is 2π divided by the coefficient of x: 2π/2 = π.

The equation of the axis is any added constant: y = 0.

The range is the axis value ± the amplitude value: from -3 to +3.

4 0

3 years ago