All categories

2 years ago

At an angle of elevation 610

Mathematics

1 answer:

Vadim26 [7]2 years ago

5 0

Answer:

The height of the cliff CD is approximately 539.76 m

Step-by-step explanation:

The given parameters are;

The first angle of elevation with which the captain sees the person on the cliff = 61°

The second angle of elevation with which the captain sees the person on the cliff after moving 92 m closer to the cliff = 69°

The angle made by the adjacent supplementary angle to the second angle of elevation = 180° - 69° = 111°

∴ Whereby, the rays from the first and second angle of elevation and the distance the ship moves closer to the cliff forms an imaginary triangle, we have;

The angle in the imaginary triangle subtended by the distance the ship moves closer to the cliff = 180° - 111° - 61° = 8°

By sine rule, we have;

AB/(sin(a)) = BC/(sin(c))

Which gives;

92/(sin(8°)) = BC/(sin(61°))

BC = (sin(61°)) × 92/(sin(8°)) ≈ 578.165 m

BC ≈ 578.165 m

The height CD = BC × sin(69°)

∴ The height of the cliff CD = 578.165 m × sin(69°) ≈ 539.76 m.

The height of the cliff CD ≈ 539.76 m.

You might be interested in

The rate of growth of profit (in millions) from an invention is approximated by Upper P prime (x )equals x e Superscript negati

Alecsey [184]

Answer:

The function is $P(x) = \frac{1}{2} e^{-x^2} +0.016$

Step-by-step explanation:

From the question we are told that

The rate of growth is $P'(x) = xe^{x} - x^2$

The total profit is $P(2) =$ $25,000

The time taken to make the profit is $x = 2 \ years$

From the question

$P'(x) = xe^{-x^2}$ is the rate of growth

Now here x represent the time taken

Now the total profit is mathematically represented as

$P(x) = \int\limits {P'(x)} \, = \int\limits {xe^{-x^2}} \,$

So using substitution method

We have that

$u = - x^2$

$du = 2xdx$

$p(x) = \int\limits {\frac{1}{2} e^{-u}} \, du$

$p(x) = {\frac{1}{2} [ e^{-u}} +c ]$

$p(x) = {\frac{1}{2} e^{-x^2}} + \frac{1}{2} c$ recall $u = - x^2$ and let $\frac{1}{2} c = Z$

At x = 2 years

$P(x) =$ $25,000

Since the profit rate is in million

$P(x) =$ $25,000 = $\frac{25000}{1000000} =$ $0.025 millon dollars

$0.025 = {\frac{1}{2} e^{-2^2}} + Z$

=> $Z = 0.025 - {\frac{1}{2} e^{-2^2}}$

$Z = 0.016$

So the profit function becomes

$P(x) = \frac{1}{2} e^{-x^2} +0.016$

5 0

3 years ago

What is the relationship between the segment pq and p’q’

worty [1.4K]

Answer:

the parallel lines match up, and the angles are the same

Step-by-step explanation:

4 0

2 years ago

Read 2 more answers

Which two ratios represent quantities that are proportional?

vesna_86 [32]

Answer:

Step-by-step explanation:

4 0

2 years ago

in chemistry class Andrew has earned scores of 64 69 and 73 on three tests he must maintain an average of 72

olganol [36]

You haven't told me what the question is. But I put the mouse
to my forehead, closed my eyes, took a deep breath, and I could
see it shimmering in my mind's eye. It was quite fuzzy, but I think
the question is

   "What score does Andrew need on the next test
   in order to raise his average to 72% ?"

The whole experience drew an incredible amount of energy
out of me, and the mouse is a total wreck. So we'll just go ahead
and answer that one. I hope it's the correct question.

The average score on 4 tests is

   (1/4) (the sum of all the scores) .

In order for Andrew to have a 72% average on 4 tests,
the sum of the 4 scores must be

   (4) x (72%) = 288% .

Out of that total that he needs, he already has

(64% + 69% + 73%) = 206%

on the first three tests.

So in order to average 72% for all 4 tests,
he'll need to score

   (288% - 206%) = 82%

on the fourth one.

6 0

2 years ago

ASAP!!!!!!!!! Please show process!!! Using law of sines!!!!!!!! Thank you so much

Flauer [41]

Answer:

the answers are on the picture but the numbers may be rounded

4 0

2 years ago