Help please with an explanation

A person is watching a boat from the top of a lighthouse. The boat is approaching the lighthouse directly. When first noticed, t

tatyana61 [14]

The boat's travel from when it was first noticed until it stopped is 554.89 ft.

<h3>What is trigonometry?</h3>

Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.

We have:

A person is watching a boat from the top of a lighthouse. The boat is approaching the lighthouse directly.

From the given information we can draw a right-angle triangle.

14°52' = 14 + 0.86 = 14.86 degree

45°10' = 45 + 0.16 = 45.16 degree

In the right-angle triangle ACD

tan14.86 = 200/AC

AC = 753.772 ft

In the right-angle triangle DBC:

tan45.16 = 200/CB

CB = 198.886 ft

AB = AC - CB

AB = 753.772 ft - 198.886 ft

AB = 554.886 ≈ 554.89 ft

Thus, the boat's travel from when it was first noticed until it stopped is 554.89 ft.

Learn more about trigonometry here:

brainly.com/question/26719838

#SPJ1

4 0

2 years ago

Two circles with different radii have chords AB and CD, such that AB is congruent to CD. Are the arcs intersected by these chord

emmainna [20.7K]

The arcs intersected by these chords are not congruent.

Given that two circles with different radii have chords AB and CD, such that AB is congruent to CD.

Let r₁ and r₂ be the radii of two different circles with centers O and O' respectively.

Assuming that the each of the ∠АОВ and ∠CO'D is less than or equal to π.

Then, we have isosceles triangle AOB and CO'D such that,

AO = OB = r₁,

CO' = O'D = r₂,

Let us assume that r₁< r₂;

We can see that arc(AB) intersected by AB is greater than arc(CD), intersected by the chord CD;

arc(AB) > arc(CD) .......(1)

Indeed,

arc(AB) = r₁ angle (AOB)

arc(CD) = r₂ angle (CO'D)

So, we have to prove that ;

∠AOB >∠CO'D ......(2)

Since each angle is less than or equal to π, and so

∠AOB/2 and ∠CO'D/2 is less than or equal to π

it suffices to show that :

tan(AOB/2) >tan(CO'D/2) ......(3)

From triangle AOB :

tan(AOB/2) = AB/(2*r₁)

tan(CO'D/2) = CD/(2*r₂)

Since AB = CD and r₁ < r₂ (As obtained from the result of (3) ), therefore, arc(AB) > arc(CD).

Hence, for two circles with different radii have chords AB and CD, such that AB is congruent to CD but the arcs intersected by these chords are not congruent.

Learn more about congruent from here brainly.com/question/1675117

#SPJ1

6 0

1 year ago

It took Joe 3 hours swimming at a speed of 12 miles per hour to swim along the Charles River. If Jennifer is swimming the same p

polet [3.4K]

Answer:

4 hours

Step-by-step explanation:

3 x 12 = 36

36/9 = 4

7 0

3 years ago

Can you please help me out?

larisa86 [58]

Answer:

- 3.5229

Step-by-step explanation:

Using the rules of logarithms

logx + logy = log(xy)

$log_{10}$ $10^{n}$ = n

Given

$log_{10}$ 3 ≈ 0.4771, then

$log_{10}$ 0.0003

= $log_{10}$ (3 × $10^{-4}$ )

= $log_{10}$ 3 + $log_{10}$ $10^{-4}$

≈ 0.4771 - 4

≈ - 3.5229 ( to 4 dec. places )

8 0

3 years ago

PLEASE ANSWER ASAP!!!

Vesna [10]

Answer:

C=x (x+3)

Step-by-step explanation:

x cannot divide x+3 definitely so the denominators must be multiplied to get the least common denominator.

4 0

3 years ago